CUET UG Applied Mathematics Booster Test 3 - Interest Rates and Compound Annual Growth Rate (CAGR) -

🚀

CUET UG Applied Mathematics Booster Test 3 - Interest Rates and Compound Annual Growth Rate (CAGR)

⏱️ 30 Minutes

❓ 20 Questions

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

CUET UG Applied Mathematics Booster Test 3 - Interest Rates and Compound Annual Growth Rate (CAGR)

1 / 20

QUESTION 1 OF 20

At what nominal rate converted semi-annually will the present value of a perpetuity of ₹450 payable at the end of every 6 months be ₹20,000?

Answer Review

1 At what nominal rate converted semi-annually will the present value of a perpetuity of ₹450 payable at the end of every 6 months be ₹20,000?

A 4.0%

B 5.0%

C 4.5%

D 6.0%

💡 Short Explanation

Use the present value formula for an end-period perpetuity. First determine the periodic interest rate. Convert it into the nominal annual rate. The borrower actually receives ₹1,800. The loan lasts for six months. Convert the six-month return into an annual effective rate.

✅ Correct Answer Explanation

For an end-period perpetuity, P = R / i where: • P = ₹20,000 • R = ₹450 Therefore, i = R / P = 450 / 20,000 = 0.0225 This is the semi-annual rate (2.25%). The nominal annual rate convertible semi-annually is r = 2 × 2.25% = 4.5% Hence, r = 4.5%. Therefore, Option C is correct. The borrower receives 2000 − 200 = 1800 The six-month interest rate is 200 / 1800 = 0.1111 The annual effective rate is r_eff = (1.1111)^2 − 1 Calculating, (1.1111)^2 = 1.2345 Hence, r_eff = 1.2345 − 1 = 0.2345 Therefore, r_eff = 23.45%. Thus, Option A is correct.

❓ Why Other Options Are Incorrect

Option A: 4.0%
Incorrect because it gives a semi-annual rate of only 2%.
Option B: 5.0%
Incorrect because it corresponds to a semi-annual rate of 2.5%.
Option D: 6.0%
Incorrect because it gives a much larger periodic interest rate.
Option B: 20.00%
Incorrect because it ignores effective annual compounding.
Option C: 21.00%
Incorrect because it underestimates the annual effective rate.
Option D: 25.00%
Incorrect because it exceeds the calculated value.

🎯 Strategy

used

Substitution

Application:

Substitute the actual amount received into the effective rate formula.

Final Logic:

Since
(1.1111)^2 − 1 = 23.45%
Option A is correct.

🧠 Memory Trick

"Advance deduction → Actual Loan Received."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Effective Interest Rate

2 Mr. X takes a loan of ₹2,000 for 6 months. The lender deducts ₹200 in advance. Using
r_"eff" =(1ⓜ+200/1800)^2-1,
find the effective annual rate.

A 23.45%

B 20.00%

C 21.00%

D 25.00%

💡 Short Explanation

The borrower actually receives ₹1,800.
The loan lasts for six months.
Convert the six-month return into an annual effective rate.

✅ Correct Answer Explanation

The borrower receives

2000 − 200 = 1800

The six-month interest rate is

200 / 1800 = 0.1111

The annual effective rate is

r_eff = (1.1111)^2 − 1

Calculating,

(1.1111)^2 = 1.2345

Hence,

r_eff = 1.2345 − 1 = 0.2345

Therefore,

r_eff = 23.45%.

Thus, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: 20.00%

Incorrect because it ignores effective annual compounding.

Option C: 21.00%

Incorrect because it underestimates the annual effective rate.

Option D: 25.00%

Incorrect because it exceeds the calculated value.

🎯 Strategy

Substitution

Application:

Substitute the actual amount received into the effective rate formula.

Final Logic:

Since

(1.1111)^2 − 1 = 23.45%

Option A is correct.

🧠 Memory Trick

"Advance deduction → Actual Loan Received."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Effective Interest Rate

3 If the cash equivalent of a perpetuity of ₹300 payable at the end of each quarter is ₹24,000, find the rate of interest compounded quarterly.

A 4%

B 6%

C 8%

D 5%

💡 Short Explanation

Use the perpetuity formula. Find the quarterly interest rate. Convert it to the nominal annual rate.

✅ Correct Answer Explanation

For an end-period perpetuity, P = R / i where: • P = ₹24,000 • R = ₹300 Thus, i = 300 / 24,000 = 0.0125 This is the quarterly interest rate (1.25%). The nominal annual rate compounded quarterly is r = 4 × 1.25% = 5% Hence, r = 5%. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 4%
Incorrect because it gives only a 1% quarterly rate.
Option B: 6%
Incorrect because it gives a 1.5% quarterly rate.
Option C: 8%
Incorrect because it gives a 2% quarterly rate.

🎯 Strategy

used

Formula Rearrangement

Application:

Calculate the quarterly rate first, then multiply by four.

Final Logic:

Since
4 × (300 / 24,000) = 5%
Option D is correct.

🧠 Memory Trick

"Quarterly Nominal = 4 × Quarterly Rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Perpetuity and Nominal Interest Rate

4 The present value of a perpetual income of ₹x payable at the end of each 6 months is ₹36,000. If the interest rate is 6% per annum compounded semi-annually (i.e., (i=0.03)), find the value of (x).

A ₹1,000

B ₹1,080

C ₹1,120

D ₹1,200

💡 Short Explanation

Use the perpetuity formula. Multiply the present value by the periodic interest rate. The periodic payment is ₹1,080.

✅ Correct Answer Explanation

For an ordinary perpetuity, P = R / i where: • P = ₹36,000 • i = 0.03 Rearranging, R = P × i Substituting, R = 36,000 × 0.03 = 1,080 Therefore, x = ₹1,080. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹1,000
Incorrect because it is less than the calculated payment.
Option C: ₹1,120
Incorrect because it exceeds the correct value.
Option D: ₹1,200
Incorrect because it overestimates the payment.

🎯 Strategy

used

Formula Rearrangement

Application:

Rearrange
P = R / i
to obtain
R = P × i

Final Logic:

Since
36,000 × 0.03 = 1,080,
Option B is correct.

🧠 Memory Trick

"Perpetuity Payment = Present Value × Interest Rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Perpetuity

5 A machine costs ₹1,00,000, has a life of 12 years, and a scrap value of ₹5,000. A sinking fund is created at 5% effective interest to accumulate ₹95,000. What is the required annual deposit?

A ₹5,968.80

B ₹5,500.00

C ₹6,000.00

D ₹5,800.50

💡 Short Explanation

First determine the amount to be accumulated. Use the sinking fund formula. The annual deposit required is ₹5,968.80.

✅ Correct Answer Explanation

The required accumulation is A = 1,00,000 − 5,000 = 95,000 For a sinking fund, R = A / S_(12|0.05) where S_(12|0.05) = ((1 + i)^n − 1) / i Here: • A = ₹95,000 • i = 0.05 • n = 12 Using S_(12|0.05) ≈ 15.9156, we obtain R = 95,000 / 15.9156 ≈ 5,968.80 Therefore, R = ₹5,968.80. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹5,500.00
Too small to accumulate ₹95,000.
Option C: ₹6,000.00
Slightly larger than the calculated value.
Option D: ₹5,800.50
Below the required annual deposit.

🎯 Strategy

used

Sinking Fund Formula

Application:

Find the amount to accumulate and divide it by the future value annuity factor.

Final Logic:

Since
95,000 / 15.9156 ≈ 5,968.80
Option A is correct.

🧠 Memory Trick

"Deposit = Target Amount ÷ Sinking Fund Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Sinking Fund

6 XYZ Company borrows ₹3,00,000 at 7% per annum for 4 years. Calculate the EMI using the reducing balance method.

A ₹7,000

B ₹7,500

C ₹7,179

D ₹8,000

💡 Short Explanation

Use the reducing balance (amortization) formula. Monthly compounding and monthly EMIs are assumed. The EMI is approximately ₹7,179.

✅ Correct Answer Explanation

For an amortized loan, R = P / a_(48|0.005833) or equivalently, R = P × [i(1 + i)^n] / [(1 + i)^n − 1] where: • P = ₹3,00,000 • i = 0.07 / 12 = 0.005833 • n = 4 × 12 = 48 Substituting these values, R ≈ ₹7,179 Therefore, EMI ≈ ₹7,179. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹7,000
Lower than the calculated EMI.
Option B: ₹7,500
Higher than the calculated EMI.
Option D: ₹8,000
Significantly higher than the required EMI.

🎯 Strategy

used

Loan Amortization Formula

Application:

Use the reducing balance EMI formula with monthly interest and monthly instalments.

Final Logic:

Applying the amortization formula gives an EMI of approximately
₹7,179
Hence, Option C is correct.

🧠 Memory Trick

"Reducing Balance EMI = Loan ÷ Present Value Annuity Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Reducing Balance (Amortized Loan)

7 A ₹10,00,000 house requires a down payment of ₹2,00,000. The remaining ₹8,00,000 is amortized at 9% per annum compounded monthly for 25 years (300 months) with an EMI of ₹6,713.57. What is the total interest paid?

A ₹10,00,000

B ₹12,14,071

C ₹11,00,000

D ₹15,00,000

💡 Short Explanation

Total repayment equals EMI multiplied by the number of instalments. Total interest equals total repayment minus the principal. The total interest is ₹12,14,071.

✅ Correct Answer Explanation

For an amortized loan, Total Interest = nR − P where: • P = ₹8,00,000 • R = ₹6,713.57 • n = 300 Total repayment is 300 × 6,713.57 = 20,14,071 Therefore, Total Interest = 20,14,071 − 8,00,000 = 12,14,071 Hence, Total Interest = ₹12,14,071. Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹10,00,000
Incorrect because it is not obtained from the amortization formula.
Option C: ₹11,00,000
Incorrect because it underestimates the total interest.
Option D: ₹15,00,000
Incorrect because it exceeds the calculated value.

🎯 Strategy

used

Loan Amortization Formula

Application:

Calculate total repayment first and then subtract the principal.

Final Logic:

Since
300 × 6,713.57 − 8,00,000 = 12,14,071
Option B is correct.

🧠 Memory Trick

"Total Interest = (EMI × Number of Instalments) − Loan Amount."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Amortized Loans

8 A bond has a face value of ₹1000, matures in 15 years, carries a nominal coupon rate of 10%, and has a yield rate of 8%. What is its purchase price?

A ₹1,000.00

B ₹1,100.50

C ₹1,200.00

D ₹1,171.19

💡 Short Explanation

The purchase price equals the present value of all coupon payments plus the present value of the redemption value. Since the coupon rate exceeds the yield rate, the bond sells at a premium. The purchase price is ₹1,171.19.

✅ Correct Answer Explanation

Coupon payment: R = 1000 × 10% = 100 The bond price is V = R × a_(15|0.08) + 1000(1.08)^(-15) Using standard annuity factors, a_(15|0.08) ≈ 8.5595 and (1.08)^(-15) ≈ 0.3152 Therefore, V = 100(8.5595) + 1000(0.3152) ≈ 855.95 + 315.24 = 1,171.19 Hence, V = ₹1,171.19. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹1,000.00
Incorrect because the bond sells above par.
Option B: ₹1,100.50
Incorrect because it underestimates the present value.
Option C: ₹1,200.00
Incorrect because it exceeds the calculated purchase price.

🎯 Strategy

used

Present Value of Bond

Application:

Add the present value of coupon payments and redemption value.

Final Logic:

Since
V = 100a_(15|0.08) + 1000(1.08)^(-15) = 1,171.19
Option D is correct.

🧠 Memory Trick

"Coupon Rate > Yield Rate ⇒ Bond Sells at Premium."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Bond Valuation

9 Evaluate the present value of the redemption parameter
\(C(1+i)^{-n}\)
for a bond where \(C=2100\), \(i=0.10\), and \(n=10\).
(Given \(\left(1.1)^{-10},\ 0.3855\right.\))

A ₹982.40

B ₹750.00

C ₹809.55

D ₹850.50

💡 Short Explanation

Multiply the redemption value by the discount factor. This gives the present value of the redemption amount. The answer is ₹809.55.

✅ Correct Answer Explanation

The present value formula is P = C(1 + i)^(-n) Substituting, P = 2100 × 0.3855 Therefore, P = 809.55 Hence, P = ₹809.55. Thus, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹982.40
Incorrect because it uses an incorrect discount factor.
Option B: ₹750.00
Incorrect because it is below the calculated value.
Option D: ₹850.50
Incorrect because it overestimates the present value.

🎯 Strategy

used

Direct Substitution

Application:

Multiply the redemption amount by the present value factor.

Final Logic:

Since
2100 × 0.3855 = 809.55
Option C is correct.

🧠 Memory Trick

"Present Value = Future Value × Discount Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Present Value of Redemption

10 Mr. M borrows ₹10,00,000 at 9% per annum compounded monthly for 10 years. The EMI is ₹12,668. The total repayment is 120 × ₹12,668. What is the total interest paid over 10 years?

A ₹4,50,000

B ₹5,20,160

C ₹6,14,071

D ₹5,00,000

💡 Short Explanation

Calculate the total repayment. Subtract the loan amount. The difference is the total interest.

✅ Correct Answer Explanation

Total repayment is 120 × 12,668 = 15,20,160 Total interest is 15,20,160 − 10,00,000 = 5,20,160 Therefore, Total Interest = ₹5,20,160. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹4,50,000
Incorrect because it underestimates the interest.
Option C: ₹6,14,071
Incorrect because it exceeds the calculated amount.
Option D: ₹5,00,000
Incorrect because it is less than the actual interest.

🎯 Strategy

used

Loan Amortization Formula

Application:

Use
Interest = nR − P

Final Logic:

Since
120 × 12,668 − 10,00,000 = 5,20,160,
Option B is correct.

🧠 Memory Trick

"Interest = Total EMI Paid − Principal."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Total Interest on Amortized Loans

11 An investment compounds quarterly for 10 years at a nominal rate of 6% per annum. What are the total number of periods (n) and the periodic rate (i)?

A (n=40,; i=0.015)

B (n=10,; i=0.06)

C (n=20,; i=0.03)

D (n=40,; i=0.06)

💡 Short Explanation

Quarterly compounding means 4 periods per year. Multiply the number of years by 4. Divide the nominal annual rate by 4.

✅ Correct Answer Explanation

Given, Annual nominal rate r=6%=0.06, Compounding frequency m=4, Time t=10 years Total number of compounding periods is n = mt = 4 × 10 = 40 The periodic interest rate is i = r / m = 0.06 / 4 = 0.015 Hence, n = 40, i = 0.015. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Uses annual compounding instead of quarterly.
Option C: Assumes semi-annual compounding.
Option D: Uses the annual rate instead of the quarterly rate.

🎯 Strategy

used

Unit Conversion

Application:

Convert years into compounding periods and annual rate into periodic rate.

Final Logic:

Since
n = 40, i = 0.015
Option A is correct.

🧠 Memory Trick

"Quarterly = 4 periods/year ⇒ Multiply years by 4 and divide the annual rate by 4."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Nominal and Periodic Interest Rates

12 A couple buys a house for ₹12,00,000 with a down payment of ₹2,50,000. What is the starting principal value (P) to be amortized?

A ₹12,00,000

B ₹2,50,000

C ₹10,00,000

D ₹9,50,000

💡 Short Explanation

Loan amount equals purchase price minus down payment. This remaining amount is the principal to be amortized.

✅ Correct Answer Explanation

The loan principal is P = House Price − Down Payment Substituting, P = 12,00,000 − 2,50,000 = 9,50,000 Therefore, P = ₹9,50,000. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Total purchase price, not the loan.
Option B: Only the down payment.
Option C: Incorrect subtraction.

🎯 Strategy

used

Direct Subtraction

Application:

Subtract the initial payment from the purchase price.

Final Logic:

Since
12,00,000-2,50,000=9,50,000,
Option D is correct.

🧠 Memory Trick

"Loan = Price − Down Payment."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Loan Principal

13 A machine costs ₹50,000 and depreciates at 8% per annum under the Written Down Value (WDV) method. The book value at the end of the 7th year is ₹27,892.33, and at the end of the 8th year is ₹25,660.94. What is the depreciation for the 8th year?

A ₹2,500.00

B ₹2,231.39

C ₹2,000.00

D ₹2,100.00

💡 Short Explanation

Annual depreciation under WDV equals the decrease in book value during the year. Subtract the value at the end of Year 8 from the value at the end of Year 7.

✅ Correct Answer Explanation

Depreciation during the 8th year is Depreciation 27,892.33-25,660.94. Thus, =2,231.39. Therefore, Depreciation = ₹2,231.39.} Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Slightly larger than the calculated depreciation.
Option C: Too low.
Option D: Less than the actual depreciation.

🎯 Strategy

used

Difference Method

Application:

Subtract consecutive book values.

Final Logic:

Since
27,892.33-25,660.94=2,231.39,
Option B is correct.

🧠 Memory Trick

"Annual Depreciation = Previous Book Value − Current Book Value."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Written Down Value Depreciation

14 Using the same machine (₹50,000 depreciating at 8% per annum under the Written Down Value method), what is the scrap value after 10 full years?

A ₹20,000.00

B ₹25,000.00

C ₹21,719.42

D ₹22,000.00

💡 Short Explanation

Under the Written Down Value (WDV) method, depreciation is charged on the reducing balance every year. Use the WDV formula. The scrap value after 10 years is ₹21,719.42.

✅ Correct Answer Explanation

The WDV formula is Plain text: S = P(1 − r)^n where: • P = ₹50,000 • r = 8% = 0.08 • n = 10 Substituting, S = 50,000(1 − 0.08)^10 = 50,000(0.92)^10 Since (0.92)^10 ≈ 0.434388, we obtain S = 50,000 × 0.434388 = 21,719.42 Therefore, S = ₹21,719.42. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹20,000.00
Incorrect because it is lower than the calculated WDV.
Option B: ₹25,000.00
Incorrect because depreciation has reduced the value further.
Option D: ₹22,000.00
Incorrect because it is only an approximation, whereas the calculated value is ₹21,719.42.

🎯 Strategy

used

WDV Formula

Application:

Use the compound depreciation formula directly.

Final Logic:

Since
50,000(0.92)^10 = 21,719.42
Option C is correct.

🧠 Memory Trick

"WDV = Cost × ((1-r)^n)."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Written Down Value Depreciation

15 Compare two investments:
An 11% stock priced at ₹143 gives an income yield of 7.69%.
A 9.75% stock priced at ₹117 gives an income yield of 8.33%.
Which yield is numerically higher?

A 11.00%

B 9.75%

C 7.69%

D 8.33%

💡 Short Explanation

Compare the two income yields directly. The second investment provides the higher income yield.

✅ Correct Answer Explanation

The income yields are already provided: First stock: • First stock: 7.69% • Second stock: 8.33% Since 8.33% > 7.69%, the second stock has the higher income yield. Therefore, 8.33% is the correct answer. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 11.00%
Incorrect because this is the dividend rate, not the income yield.
Option B: 9.75%
Incorrect because this is the nominal dividend rate.
Option C: 7.69%
Incorrect because it is lower than 8.33%.

🎯 Strategy

used

Direct Comparison

Application:

Compare the two income yields numerically.

Final Logic:

Since
8.33%>7.69%,
Option D is correct.

🧠 Memory Trick

"Higher Yield = Better Return (for equal investment)."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Yield Comparison

16 A man buys shares of face value ₹25 paying a 9% dividend. The investment yields exactly 10%. What is the purchase price per share?

A ₹22.50

B ₹25.00

C ₹20.00

D ₹27.50

💡 Short Explanation

First calculate the annual dividend. Then divide the dividend by the required yield. The purchase price is ₹22.50.

✅ Correct Answer Explanation

Dividend per share is D = 25 × 9% = 25 × 0.09 = 2.25 Income yield is Yield = Dividend / Purchase Price Therefore, Purchase Price = 2.25 / 0.10 = 22.50 Hence, Purchase Price = ₹22.50. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹25.00
Incorrect because it gives only a 9% yield.
Option C: ₹20.00
Incorrect because it would produce an 11.25% yield.
Option D: ₹27.50
Incorrect because it gives a yield below 9%.

🎯 Strategy

used

Yield Formula

Application:

Calculate the dividend and divide it by the required yield.

Final Logic:

Since
2.25 / 0.10 = 22.50
Option A is correct.

🧠 Memory Trick

"Purchase Price = Dividend ÷ Required Yield."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Share Valuation

17 Find the total dividend income derived from 88 shares of face value ₹25 each (Total face value = ₹2,200) paying a 7.5% dividend.

A ₹150

B ₹165

C ₹180

D ₹200

💡 Short Explanation

Dividend is calculated on the face value of the shares. First calculate the total face value. Then compute 7.5% of the total face value.

✅ Correct Answer Explanation

Total face value is 88 × 25 = ₹2,200 Dividend income is Dividend = 2,200 × (7.5 / 100) Thus, = 2,200 × 0.075 = 165 Therefore, Dividend Income = ₹165. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹150
Incorrect because it underestimates the dividend.
Option C: ₹180
Incorrect because it exceeds the calculated dividend.
Option D: ₹200
Incorrect because it is much larger than the actual value.

🎯 Strategy

used

Percentage Calculation

Application:

Calculate the total face value first and then find the specified percentage.

Final Logic:

Since
2,200 × 7.5% = 165
Option B is correct.

🧠 Memory Trick

"Dividend = Face Value × Dividend Rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Shares and Dividend

18 A sinking fund is required to replace a ₹50,000 machine (salvage value ₹5,000) over 10 years. The total amount to be accumulated is ₹45,000. Calculate the quarterly payment at 8% per annum compounded quarterly.

A ₹650

B ₹800

C ₹745

D ₹900

💡 Short Explanation

The sinking fund must accumulate ₹45,000. Quarterly deposits are made for 40 quarters. Using the sinking fund formula gives a quarterly payment of approximately ₹745.

✅ Correct Answer Explanation

The amount to be accumulated is A = 50,000 − 5,000 = 45,000 Quarterly interest rate: i = 8% / 4 = 0.02 Number of quarters: n = 10 × 4 = 40 The sinking fund formula is R = A / S_(40|0.02) where S_(40|0.02) = ((1 + i)^n − 1) / i Using S_(40|0.02) ≈ 60.40, we obtain R = 45,000 / 60.40 ≈ 744.9 Therefore, R ≈ ₹745. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹650
Too low to accumulate ₹45,000.
Option B: ₹800
Higher than the calculated deposit.
Option D: ₹900
Significantly higher than required.

🎯 Strategy

used

Sinking Fund Formula

Application:

Use the accumulated amount, quarterly rate, and total quarters.

Final Logic:

Since
45,000 / 60.40 ≈ 745
Option C is correct.

🧠 Memory Trick

"Quarterly Deposit = Target Amount ÷ Sinking Fund Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Sinking Fund

19 What is the present value of a perpetuity of ₹1,800 payable at the end of each quarter forever at 5% per annum compounded quarterly?

A ₹1,44,000

B ₹1,20,000

C ₹1,35,000

D ₹1,00,000

💡 Short Explanation

Use the perpetuity formula. Convert the annual nominal rate into a quarterly rate. Divide the quarterly payment by the quarterly interest rate.

✅ Correct Answer Explanation

The quarterly interest rate is i = 5% / 4 = 0.0125 For an ordinary perpetuity, P = R / i Substituting, P = 1,800 / 0.0125 = 1,44,000 Therefore, P = ₹1,44,000. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹1,20,000
Uses an incorrect interest rate.
Option C: ₹1,35,000
Underestimates the perpetuity value.
Option D: ₹1,00,000
Much smaller than the correct present value.

🎯 Strategy

used

Perpetuity Formula

Application:

Convert the annual rate into a quarterly rate and apply
P = R / i

Final Logic:

Since
1,800 / 0.0125 = 1,44,000,
Option A is correct.

🧠 Memory Trick

"Perpetuity = Payment ÷ Periodic Interest Rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Perpetuity

20 Find the present value of a perpetuity of ₹780 payable at the beginning of each year at 6% effective interest.

A ₹13,000

B ₹14,000

C ₹12,780

D ₹13,780

💡 Short Explanation

This is a perpetuity due because payments occur at the beginning of each year. Use the perpetuity due formula. The present value is ₹13,780.

✅ Correct Answer Explanation

For a perpetuity due, Plain text: P = R + (R / i) = R(1 + 1 / i) Here: • R = ₹780 • i = 0.06 Thus, P = 780(1 + 1 / 0.06) = 780(17.6667) = 13,780 Therefore, P = ₹13,780. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹13,000
Lower than the calculated value.
Option B: ₹14,000
Slightly higher than the correct value.
Option C: ₹12,780
Omits the additional first payment made immediately.

🎯 Strategy

used

Perpetuity Due Formula

Application:

Since payments begin immediately, use
P = R + (R / i)

Final Logic:

Since
780 + (780 / 0.06) = 13,780,
Option D is correct.

🧠 Memory Trick

"Beginning Payment ⇒ Add One Extra Payment."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Perpetuity Due

CUET UG Applied Mathematics Booster Test 3 - Interest Rates and Compound Annual Growth Rate (CAGR)

Test Complete!

Answer Review