CUET UG Applied Mathematics Booster Test 2 - Bonds, Yield and Bond Valuation -

🚀

CUET UG Applied Mathematics Booster Test 2 - Bonds, Yield and Bond Valuation

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 2 - Bonds, Yield and Bond Valuation

1 / 20

QUESTION 1 OF 20

Arrange the sequence of events in the standard life cycle of a bond:
1. Borrower promises to pay a specified sum at maturity.
2. Bond is redeemed (repaid) at par or premium.
3. A written contract is established between borrower and lender.
4. Interest payments are made at equal mathematical intervals.

Answer Review

1 Arrange the sequence of events in the standard life cycle of a bond:
1. Borrower promises to pay a specified sum at maturity.
2. Bond is redeemed (repaid) at par or premium.
3. A written contract is established between borrower and lender.
4. Interest payments are made at equal mathematical intervals.

A 1, 3, 4, 2

B 3, 1, 4, 2

C 3, 4, 1, 2

D 1, 4, 3, 2

💡 Short Explanation

The bond contract is created first. The borrower agrees to repay the principal. Interest is paid periodically until redemption.

✅ Correct Answer Explanation

The normal life cycle of a bond follows this order: Step 1: A written contract is established between the borrower and the lender. Step 2: The borrower promises to repay the specified principal amount on the maturity date. Step 3: During the life of the bond, periodic coupon (interest) payments are made at fixed intervals. Step 4: On maturity, the bond is redeemed at par or at the agreed redemption value. Therefore, the correct sequence is 3→1→4→2 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 1, 3, 4, 2
Incorrect because the written contract must exist before any repayment promise.
Option C: 3, 4, 1, 2
Incorrect because the repayment promise forms part of the contract before interest payments begin.
Option D: 1, 4, 3, 2
Incorrect because the contract cannot be established after interest payments have begun.

🎯 Strategy

used

Elimination

Application:

Arrange the events according to the chronological sequence of a standard bond transaction.

Final Logic:

Contract → Promise → Interest Payments → Redemption; therefore Option B.

🧠 Memory Trick

"Contract → Promise → Coupon → Redemption."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Definition of Bond

2 Assertion (A):
A bond contract strictly prohibits the payment of interest at equal intervals.
Reason (R):
Bonds are only issued for infinite periods, making periodic redemption impossible.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Bonds generally pay periodic coupon interest. Most bonds have a fixed maturity date. Therefore, both statements are incorrect.

✅ Correct Answer Explanation

The Assertion is false because a standard bond contract requires the issuer to pay periodic coupon interest at equal intervals, such as annually or semi-annually. The Reason is also false because bonds are generally issued for a fixed maturity period, after which they are redeemed. Only a few special instruments, such as perpetual bonds, have no maturity date. Therefore, both the Assertion and the Reason are false. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: A is true, R is false.
Incorrect because the assertion itself is false.
Option C: Both A and R are true.
Incorrect because neither statement is correct.
Option D: A is false, R is true.
Incorrect because the reason incorrectly states that all bonds have infinite lives.

🎯 Strategy

used

Elimination

Application:

Recall the essential features of a standard bond regarding coupon payments and maturity.

Final Logic:

Since bonds normally pay periodic interest and have fixed maturity dates, both statements are false; therefore Option A.

🧠 Memory Trick

"Bond = Coupons + Maturity."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Bond Contract Features ═════════════════════════════════════════════════════

3 If the face value (F) of a standard bond is plotted against time on a Cartesian plane (Time on X-axis, Face Value on Y-axis), what is the expected shape of the graph?

A An upward sloping straight line

B A downward sloping parabola

C An oscillating sine wave

D A straight line parallel to the X-axis

💡 Short Explanation

Face value is fixed throughout the bond's life. It does not change with time. Therefore, its graph is a horizontal line.

✅ Correct Answer Explanation

The face value (par value) of a bond is determined when the bond is issued and remains constant until redemption. If time is plotted on the x-axis and face value on the y-axis, then F= Constant A constant function is represented graphically by a horizontal straight line, which is parallel to the x-axis. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: An upward sloping straight line.
Incorrect because the face value does not increase over time.
Option B: A downward sloping parabola.
Incorrect because the face value does not vary quadratically.
Option C: An oscillating sine wave.
Incorrect because the face value does not fluctuate periodically.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that the face value remains constant throughout the life of the bond.

Final Logic:

A constant quantity is represented by a horizontal line; therefore Option D.

🧠 Memory Trick

"Face Value Never Changes."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Face Value

4 Four different bonds have redemption values of ₹100, ₹105, ₹110, and ₹105. What is the moving average of size 2 for the last two bonds?

A ₹102.5

B ₹105.0

C ₹107.5

D ₹110.0

💡 Short Explanation

A moving average of size 2 uses the last two observations. Average the redemption values ₹110 and ₹105. The result is ₹107.5.

✅ Correct Answer Explanation

A moving average of size 2 for the final observation is calculated using the last two redemption values. Thus, (110 + 105) / 2 = 215 / 2 = 107.5 Therefore, the moving average for the last two bonds is ₹107.5 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹102.5
Incorrect because it is not the average of the last two redemption values.
Option B: ₹105.0
Incorrect because it equals one redemption value rather than the moving average.
Option D: ₹110.0
Incorrect because it represents only one observation.

🎯 Strategy

used

Substitution

Application:

Take the last two observations and compute their arithmetic mean.

Final Logic:

Since
(110 + 105) / 2 = 107.5
Option C is correct.

🧠 Memory Trick

"Moving Average = Average of Latest Values."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Redemption Value ═════════════════════════════════════════════════════

5 Let the vector be defined as
\(\vec{P}=[P_{0},F],\)
where (P_0) is the market price and (F) is the face value. Which scalar condition represents a bond selling at a discount?

A \(P_{0}-F=0\)

B \(P_{0}-F>0\)

C \(P_{0}-F<0\)

D \(P_{0}⋅F=1\)

💡 Short Explanation

A discount bond sells below face value. Therefore, market price is less than face value. Their difference is negative.

✅ Correct Answer Explanation

A bond sells at a discount when P₀ < F where: P₀ = Market price F = Face value Subtracting F from both sides, P₀ − F < 0 Thus, the scalar condition representing a discount bond is P₀ − F < 0 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: (P_0-F=0)
Incorrect because this represents a bond selling at par.
Option B: (P_0-F>0)
Incorrect because this represents a premium bond.
Option D: (P_0\cdot F=1)
Incorrect because the product of the prices has no significance in identifying discount bonds.

🎯 Strategy

used

Elimination

Application:

Recall the mathematical definition of a discount bond and eliminate conditions representing par and premium.

Final Logic:

A discount bond satisfies
P₀ < F ⇒ P₀ − F < 0
therefore Option C.

🧠 Memory Trick

"Discount = Market < Face."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Discount Bond ═════════════════════════════════════════════════════

6 If the premium value over time is modeled by the function
\(P(t)=5e^{0.02t},\)
what does the definite integral
\(\int_{0}^{10}\,5e^{0.02t} dt\)
represent?

A The instantaneous premium at (t=10)

B The face value of the bond at maturity

C The yield to maturity as a continuous rate

D The total accumulated premium over 10 years (area under the curve)

💡 Short Explanation

A definite integral gives the area under a curve. The curve represents premium over time. Therefore, the integral gives the accumulated premium.

✅ Correct Answer Explanation

The function P(t) = 5e^(0.02t) represents the premium value at time t. The definite integral ∫₀¹⁰ 5e^(0.02t) dt computes the area under the premium curve from (t=0) to (t=10). This area represents the total accumulated premium over the 10-year period. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: The instantaneous premium at (t=10)
Incorrect because this would be obtained by evaluating (P(10)), not by integration.
Option B: The face value of the bond at maturity.
Incorrect because the integral does not determine the face value.
Option C: The yield to maturity as a continuous rate.
Incorrect because the integral measures accumulated quantity, not yield.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recall that a definite integral represents the accumulated value or area under a function.

Final Logic:

A definite integral gives the accumulated premium over time; therefore Option D.

🧠 Memory Trick

"Integral = Area = Accumulation."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Premium Concept

7 If discrete coupon payments (C) are represented as rectangles of height (C) and width 1 year on a graph, what does the total area of (n) such rectangles represent?

A Total undiscounted coupon payments over (n) years

B Exact present value of the bond

C Yield to maturity limit

D Compounded nominal rate area

💡 Short Explanation

Each rectangle represents one year's coupon payment. Area of one rectangle equals (C \times 1=C). Total area equals the total coupon payments received.

✅ Correct Answer Explanation

Each rectangle has Height = (C) (annual coupon payment), Width = (1) year. Therefore, the area of one rectangle is C × 1 = C For (n) years, the total area is nC which represents the total undiscounted coupon payments received over the bond's life. Since no discounting is applied, this is not the present value of the bond. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Exact present value of the bond.
Incorrect because present value requires discounting future coupon payments.
Option C: Yield to maturity limit.
Incorrect because the area represents cash flow, not yield.
Option D: Compounded nominal rate area.
Incorrect because the graph represents coupon payments rather than compound interest.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Interpret the geometric meaning of area as the accumulation of equal annual coupon payments.

Final Logic:

The sum of the rectangle areas equals the total undiscounted coupon payments; therefore Option A.

🧠 Memory Trick

"Area = Total Coupons."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Coupon Rate ═════════════════════════════════════════════════════

8 An investor randomly selects one bond from a set of 5 bonds. Among them, 3 bonds have a nominal rate of 8% and 2 bonds have a nominal rate of 10%. What is the probability that the selected bond has a nominal rate of 8%?

A \(\frac{3}{8}\)

B \(\frac{3}{5}\)

C \(\frac{2}{5}\)

D \(\frac{1}{5}\)

💡 Short Explanation

Count the favorable outcomes. Divide by the total number of bonds. Simplify the probability.

✅ Correct Answer Explanation

The probability of selecting a bond with an 8% nominal rate is Probability = Number of Favorable Bonds / Total Number of Bonds Here, Favorable bonds = 3 Total bonds = 5 Therefore, P = 3/5 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: (\frac{3}{8})
Incorrect because the denominator should be the total number of bonds (5), not 8.
Option C: (\frac{2}{5})
Incorrect because this is the probability of selecting a 10% bond.
Option D: (\frac{1}{5})
Incorrect because only one favorable outcome is not available.

🎯 Strategy

used

Substitution

Application:

Apply the basic probability formula using the given frequencies.

Final Logic:

Since
3/5
represents the favorable outcomes divided by the total outcomes, Option B is correct.

🧠 Memory Trick

"Probability = Favorable ÷ Total."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Nominal Rate

9 Identify the incorrect statement regarding current yield.
\(\frac{C}{P_{0}}\).

A Current yield is the coupon payment as a percentage of the current bond price.

B Current yield is always equal to yield to maturity regardless of price.

C Current yield is given by

D When a bond sells at par, current yield equals coupon yield.

💡 Short Explanation

Current yield depends on market price. Yield to maturity generally differs from current yield. They become equal only when special conditions apply.

✅ Correct Answer Explanation

The current yield of a bond is Current Yield = C / P₀ where (C) = Annual coupon payment, (P_0) = Current market price. Yield to Maturity (YTM) considers coupon payments, redemption value, time to maturity, and purchase price, making it different from current yield in most situations. Only under particular circumstances (such as a bond purchased at par with matching coupon and market yields) may current yield equal YTM. Therefore, the statement that current yield is always equal to YTM is incorrect. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Current yield is the coupon payment as a percentage of the current bond price.
Correct because this is the standard definition.
Option C: Current yield is given by
C / P₀
Correct because it is the mathematical formula for current yield.
Option D: When a bond sells at par, current yield equals coupon yield.
Correct because when
P₀ = F
the current yield equals the coupon rate.

🎯 Strategy

used

Elimination

Application:

Recall the definitions of current yield and YTM, then eliminate the correct statements.

Final Logic:

Current yield is not always equal to YTM; therefore Option B is the incorrect statement.

🧠 Memory Trick

"Current ≠ YTM (Usually)."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Current Yield ═════════════════════════════════════════════════════

10 Which of the following conditions must be satisfied for an investor to realize a return exactly equal to the Yield to Maturity (YTM)?
I. Buy the bond at current price P₀
II. Hold the bond until maturity
III. Sell the bond immediately at a premium
IV. Redeem the bond at par

A I, II only

B II, III, IV

C I, II, IV

D I, III, IV

💡 Short Explanation

Purchase the bond at its current market price. Hold it until maturity. Receive the redemption value at maturity.

✅ Correct Answer Explanation

Yield to Maturity (YTM) represents the annual return an investor earns if the bond is purchased at the current market price and held until maturity. For the realized return to equal the quoted YTM: Statement I is correct because the investor must purchase the bond at the prevailing market price. Statement II is correct because YTM assumes the bond is held until maturity. Statement III is incorrect because selling the bond immediately prevents the investor from receiving all future coupon payments and the redemption amount. Statement IV is correct because the investor receives the redemption value (par value in this case) at maturity. Therefore, the correct combination is I, II, and IV. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: I, II only.
Incorrect because redemption at maturity is also part of realizing the YTM.
Option B: II, III, IV.
Incorrect because selling immediately is inconsistent with the definition of YTM.
Option D: I, III, IV.
Incorrect because selling immediately prevents realization of the full YTM.

🎯 Strategy

used

Elimination

Application:

Recall the assumptions underlying the definition of Yield to Maturity and eliminate any condition that violates them.

Final Logic:

YTM is realized only when the bond is bought at the market price, held until maturity, and redeemed; therefore Option C.

🧠 Memory Trick

"Buy → Hold → Redeem = YTM."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Yield to Maturity

11 A bond is currently selling at a discount. The coupon yield is 6% and the current yield is 7%. Which of the following values is a valid Yield to Maturity (YTM), based on the inequality relationship
\(Coupon Yield<Current Yield<YTM\)

A (8.0%)

B (6.5%)

C (5.0%)

D (6.0%)

💡 Short Explanation

Discount bonds satisfy Coupon Yield < Current Yield < YTM YTM must exceed 7%. Only 8% satisfies the inequality.

✅ Correct Answer Explanation

For a discount bond, the standard yield relationship is Coupon Yield < Current Yield < Yield to Maturity Given 6% < 7% < YTM the Yield to Maturity must be greater than 7%. Checking the options: (8.0%) ✓ satisfies the inequality. (6.5%) ✗ is less than the current yield. (5.0%) ✗ is even smaller. (6.0%) ✗ equals the coupon yield. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: (6.5%)
Incorrect because it is less than the current yield.
Option C: (5.0%)
Incorrect because it is less than both the coupon yield and current yield.
Option D: (6.0%)
Incorrect because it equals the coupon yield rather than exceeding the current yield.

🎯 Strategy

used

Elimination

Application:

Apply the standard inequality for discount bonds and eliminate values that do not exceed the current yield.

Final Logic:

Only (8.0%) satisfies
6% < 7% < YTM
therefore Option A.

🧠 Memory Trick

"Discount → Highest YTM."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Yield Relations for Discount Bonds ═════════════════════════════════════════════════════

12 Match the market status with the correct mathematical inequality relation.

List I	List II
1. Discount	a. YTM = Current Yield
2. Premium	b. YTM < Current Yield
3. Par	c. YTM > Current Yield

A 1–a, 2–b, 3–c

B 1–b, 2–c, 3–a

C 1–c, 2–a, 3–b

D 1–c, 2–b, 3–a

💡 Short Explanation

Discount bonds have the highest YTM. Premium bonds have the lowest YTM. Par bonds have equal current yield and YTM.

✅ Correct Answer Explanation

The standard relationships are: Discount Bond Discount Bond: YTM > Current Yield Premium Bond: YTM < Current Yield Par Bond: YTM = Current Yield Thus, the correct matching is: Discount → c Premium → b Par → a Therefore, 1 – c, 2 – b, 3 – a Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A
Incorrect because it incorrectly matches the discount bond with equal yields.
Option B
Incorrect because it reverses the premium and discount relationships.
Option C
Incorrect because a par bond satisfies equality, not (\text{YTM}<\text{Current Yield}).

🎯 Strategy

used

Option Grouping

Application:

Recall the standard yield relationships for discount, premium, and par bonds before matching.

Final Logic:

Discount → Greater, Premium → Smaller, Par → Equal; therefore Option D.

🧠 Memory Trick

"Discount ↑, Premium ↓, Par =."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Yield Relations ═════════════════════════════════════════════════════

📄 Passage

"In the present value approach, we calculate the present value of each expected cash flow. A bond or debenture often has a maturity date. Thus, the value of a bond is calculated by considering the annual interest payments plus its terminal value using the present value concept. By discounting these future cash flows using an appropriate discount rate, we determine the fair purchase price."

Under the present value approach described in the passage, what is the formula for the present value of the redemption price (C), discounted at rate (i) over (n) periods?

A \(P_{2}=C(1+i)^{-n}\)

B \(P_{2}=C(1+i)^{n}\)

C \(P_{2}=C(1-i)^{-n}\)

D \(P_{2}=\frac{C}{i}\)

💡 Short Explanation

Redemption value is received at maturity. It must be discounted to the present. Use the standard present value formula.

✅ Correct Answer Explanation

The redemption value (C) is received after (n) periods. Its present value is obtained by discounting it using the compound discount factor: P₂ = C(1 + i)⁻ⁿ Here, (C) = Redemption (maturity) value, (i) = Discount (yield) rate per period, (n) = Number of periods. This discounted redemption value is one component of the bond's total purchase price. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B:
P₂ = C(1 + i)ⁿ
Incorrect because this calculates the future value, not the present value.
Option C:
P₂ = C(1 − i)⁻ⁿ
Incorrect because the standard discounting formula uses (1+i), not (1-i).
Option D:
P₂ = C / i
Incorrect because this is related to perpetuity valuation, not redemption value.

🎯 Strategy

used

Substitution

Application:

Recall the standard present value formula for a single future payment.

Final Logic:

Future redemption values are discounted using
(1 + i)⁻ⁿ
therefore Option A.

🧠 Memory Trick

"Future ÷ Growth Factor = Present Value."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value of Redemption Value ═════════════════════════════════════════════════════

📄 Passage

Using the cash flow discounting approach, determine the purchase price of a ₹600, 8% bond, with dividends payable semi-annually, redeemable at par in 5 years, if the yield rate is 8% compounded semi-annually.

A ₹550

B ₹600

C ₹650

D ₹700

💡 Short Explanation

Coupon rate equals yield rate. Redemption is at par. Therefore, the bond sells at par.

✅ Correct Answer Explanation

Given: Face value = ₹600 Coupon rate = 8% Yield rate = 8% Redemption at par Semi-annual compounding When the coupon rate equals the yield rate, the present value of all coupon payments plus the present value of the redemption amount equals the bond's face value. Therefore, V = ₹600 Hence, the purchase price of the bond is ₹600 Thus, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹550
Incorrect because a discount price would occur only if the yield exceeded the coupon rate.
Option C: ₹650
Incorrect because a premium price would occur only if the coupon rate exceeded the yield.
Option D: ₹700
Incorrect because the bond sells at par, not at a premium.

🎯 Strategy

used

Elimination

Application:

Recognize the standard bond pricing rule when coupon rate equals the market yield.

Final Logic:

Coupon Rate = Yield Rate ⇒ Bond Price = Face Value; therefore Option B.

🧠 Memory Trick

"Coupon = Yield ⇒ Price = Par."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Bond Valuation ═════════════════════════════════════════════════════

15 Assertion (A):
The periodic dividend payment (R) is calculated by dividing the yield to maturity by the face value.
Reason (R):
The periodic dividend payment (R) is given by
\(R=C\times i_{d},\)
where (C) is the face value and (i_d) is the nominal rate of interest per period.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Coupon payment is determined using the coupon rate. YTM does not determine the coupon payment. The reason correctly states the formula.

✅ Correct Answer Explanation

The Assertion is false because the periodic coupon payment is not obtained by dividing Yield to Maturity by the face value. Instead, the coupon payment is calculated using R = C × i_d where (C) = Face value, (i_d) = Coupon (nominal) rate per period. Yield to Maturity is an investment return measure and does not determine the coupon amount. Therefore, the Reason is true. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Both A and R are false.
Incorrect because the reason correctly gives the coupon-payment formula.
Option B: A is true, R is false.
Incorrect because the assertion is false.
Option C: Both A and R are true.
Incorrect because the assertion incorrectly defines the coupon payment.

🎯 Strategy

used

Elimination

Application:

Differentiate between coupon payment and Yield to Maturity before evaluating the statements.

Final Logic:

Coupon payment depends on the nominal coupon rate, not on YTM; therefore Option D.

🧠 Memory Trick

"Coupon = Face × Coupon Rate."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Periodic Coupon Payment ═════════════════════════════════════════════════════

16 Identify the mathematically incorrect statement regarding the present value of redemption.

A P_2=C(1+i)^(-n).

B It is an essential component of the total purchase price (V).

C It represents the future compounded value of the first periodic payment.

D If the bond is redeemed at par, then (C=F).

💡 Short Explanation

Redemption value is the maturity payment. It is discounted to obtain its present value. It is not the compounded value of a coupon payment.

✅ Correct Answer Explanation

The present value of redemption is calculated by discounting the redemption (maturity) value back to the present using P₂ = C(1 + i)⁻ⁿ where (C) = Redemption value, (i) = Yield (discount) rate per period, (n) = Number of periods. This discounted redemption amount forms an important part of the bond's purchase price. The statement that it represents the future compounded value of the first periodic payment is incorrect because redemption value refers to repayment of the principal at maturity, not to any coupon payment. Therefore, Option C is the incorrect statement.

❓ Why Other Options Are Incorrect

Option A:
P₂ = C(1 + i)⁻ⁿ
Correct because this is the standard present value formula for the redemption amount.
Option B: It is an essential component of the total purchase price (V).
Correct because the purchase price equals the present value of coupons plus the present value of redemption.
Option D: If the bond is redeemed at par, then (C=F).
Correct because redemption at par means the redemption value equals the face value.

🎯 Strategy

used

Elimination

Application:

Recall the meaning of redemption value and eliminate statements that correctly describe bond valuation.

Final Logic:

Redemption value is the discounted maturity payment, not the compounded value of a coupon; therefore Option C.

🧠 Memory Trick

"Redemption = Principal, Not Coupon."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value of Redemption

17 Let \(\vec{V}_{calc}\)denote the theoretical present value and \(\vec{V}_{market}\)denote the market price. A bond is overvalued when which of the following conditions holds?

A \(∣\vec{V}_{market}∣=∣\vec{V}_{calc}∣\)

B \(∣\vec{V}_{market}∣<∣\vec{V}_{calc}∣\)

C \(∣\vec{V}_{market}∣>∣\vec{V}_{calc}∣\)

D \(∣\vec{V}_{market}∣=0\)

💡 Short Explanation

Overvaluation occurs when market price exceeds intrinsic value. Investors pay more than the theoretical value. Therefore, market value is greater than calculated value.

✅ Correct Answer Explanation

A bond is overvalued when its market price exceeds its theoretical (intrinsic) value obtained through present value calculations. Mathematically, Market Price Calculated Present Value Using the notation given, |V_market| = |V_calc| This means investors are paying more than the bond's intrinsic worth. Therefore, Option C is correct.

❓ Why Other Options Are Incorrect

Option A:
Option A:
|V_market| = |V_calc|
Incorrect because this indicates a fairly valued bond.
Option B:
|V_market| < |V_calc|
Incorrect because this represents an undervalued bond.
Option D:
|V_market| = 0
Incorrect because a bond cannot normally have a market price of zero.

🎯 Strategy

used

Elimination

Application:

Recall the relationship between intrinsic value and market price for overvalued securities.

Final Logic:

Overvalued means Market Price > Calculated Value; therefore Option C.

🧠 Memory Trick

"Market Above Value = Overvalued."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Overvaluation ═════════════════════════════════════════════════════

18 If the continuous market price is (M(t)) and the theoretical value is (T(t)), the total accumulated undervaluation over time (T) is expressed as:

A \(\int_{0}^{T}\,[M(t)+T(t)] dt\)

B \(\int_{0}^{T}\,[T(t)-M(t)] dt\), where \(T(t)>M(t)\)

C \(\int_{0}^{T}\,[M(t) T(t)] dt\)

D \(\int_{0}^{T}\,\frac{M(t)}{T(t)} dt\)

💡 Short Explanation

Undervaluation occurs when theoretical value exceeds market price. The difference represents undervaluation at each instant. Integrating gives the accumulated undervaluation.

✅ Correct Answer Explanation

At any instant, Undervaluation = T(t) − M(t) provided T(t) > M(t) The total accumulated undervaluation over the interval [0, T] is therefore ∫₀ᵀ [T(t) − M(t)] dt This integral measures the area between the theoretical value curve and the market price curve. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A:
Option B:
∫₀ᵀ [M(t) + T(t)] dt
Incorrect because adding the two values does not measure undervaluation.
Option C:
∫₀ᵀ [M(t) × T(t)] dt
Incorrect because multiplying the functions has no interpretation in bond undervaluation.
Option D:
∫₀ᵀ M(t) / T(t) dt
Incorrect because the ratio does not measure accumulated undervaluation.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that undervaluation is measured by the difference between intrinsic value and market price.

Final Logic:

Accumulated undervaluation equals the integral of (T(t)-M(t)); therefore Option B.

🧠 Memory Trick

"Value − Market = Undervaluation."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Undervaluation

19 A portfolio contains 10 corporate bonds and 2 benchmark government securities. What is the probability of randomly selecting a benchmark government security?

A \(\frac{1}{12}\)

B \(\frac{1}{5}\)

C \(\frac{5}{6}\)

D \(\frac{1}{6}\)

💡 Short Explanation

Total securities = 12. Benchmark government securities = 2. Probability equals favorable outcomes divided by total outcomes.

✅ Correct Answer Explanation

The probability of selecting a benchmark government security is Probability = Number of Benchmark Securities / Total Number of Securities Here, Benchmark government securities = 2 Total securities = 10 + 2 = 12 Therefore, P = 2/12 = 1/6 Hence, the correct answer is 1/6 Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: \(\frac{1}{12}\)
Incorrect because there are two benchmark securities, not one.
Option B: B) \(\frac{1}{5}\)
Incorrect because the denominator should be the total number of securities (12).
Option C: C) \(\frac{5}{6}\)
Incorrect because it represents the probability of not selecting a benchmark security.

🎯 Strategy

used

Substitution

Application:

Use the basic probability formula by dividing the number of favorable outcomes by the total number of outcomes.

Final Logic:

Since
2/12 = 1/6
Option D is correct.

🧠 Memory Trick

"Probability = Favorable ÷ Total."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Benchmark Comparison

20 Match the credit spread concepts.

List I	List II
1. Small spread	a. Better quality bond
2. Large spread	b. Lower quality bond
3. Yield to Maturity	c. Required return measure
4. Benchmark	d. Government security Answer: A

A 1–a, 2–b, 3–c, 4–d

B 1–b, 2–a, 3–d, 4–c

C 1–c, 2–d, 3–a, 4–b

D 1–d, 2–c, 3–b, 4–a

💡 Short Explanation

Better-quality bonds have smaller credit spreads. Lower-quality bonds require larger spreads. Government securities commonly serve as benchmarks.

✅ Correct Answer Explanation

The correct matching is: Small spread → Better quality bond because investors require only a small risk premium. Large spread → Lower quality bond because higher credit risk demands a larger premium. Yield to Maturity → Required return measure, representing the total expected annual return. Benchmark → Government security, since government bonds are commonly used as benchmark securities. Thus, the correct matching is: (1 \rightarrow a) (2 \rightarrow b) (3 \rightarrow c) (4 \rightarrow d) Hence, 1 – a, 2 – b, 3 – c, 4 – d and Option A is correct.

❓ Why Other Options Are Incorrect

Option B
Incorrect because it reverses the relationship between small and large credit spreads.
Option C
Incorrect because Yield to Maturity is not a better-quality bond, and Benchmark is not a lower-quality bond.
Option D
Incorrect because the benchmark is a government security, not a better-quality bond category.

🎯 Strategy

used

Option Grouping

Application:

Match each financial concept independently with its correct definition before selecting the complete option.

Final Logic:

Small Spread → Better Quality, Large Spread → Lower Quality, YTM → Required Return, Benchmark → Government Security; therefore Option A.

🧠 Memory Trick

"Better Bond → Smaller Spread."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Credit Spread

CUET UG Applied Mathematics Booster Test 2 - Bonds, Yield and Bond Valuation

Test Complete!

Answer Review