CUET UG Applied Mathematics Booster Test 3 - Loans, EMI and Loan Amortization -

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CUET UG Applied Mathematics Booster Test 3 - Loans, EMI and Loan Amortization

⏱️ 30 Minutes

❓ 20 Questions

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

CUET UG Applied Mathematics Booster Test 3 - Loans, EMI and Loan Amortization

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QUESTION 1 OF 20

Evaluate the following statements regarding Financial Mathematics in daily life:
I. Operations in banking use money belonging to one individual to be used by others.
II. It guarantees zero risk for lenders.
III. Periodic payments return the borrowed money.

Answer Review

1 Evaluate the following statements regarding Financial Mathematics in daily life:
I. Operations in banking use money belonging to one individual to be used by others.
II. It guarantees zero risk for lenders.
III. Periodic payments return the borrowed money.

A I only

B II and III

C I and III

D I, II, and III

💡 Short Explanation

Banking involves lending others' money. Loans are repaid through periodic payments. Financial mathematics does not eliminate lending risk.

✅ Correct Answer Explanation

Financial mathematics studies transactions involving borrowing and lending of money. Statement I is correct because banks lend money deposited by one group of individuals to borrowers. Statement II is incorrect because every loan involves some degree of credit risk; financial mathematics helps evaluate risk but cannot eliminate it. Statement III is correct because borrowers repay loans through periodic instalments consisting of principal and interest. Therefore, only Statements I and III are correct. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: I only.
Incorrect because Statement III is also correct.
Option B: II and III.
Incorrect because Statement II is false.
Option D: I, II, and III.
Incorrect because Statement II is incorrect.

🎯 Strategy

used

Elimination

Application:

Evaluate each statement independently using basic loan concepts.

Final Logic:

Only Statements I and III are true; therefore Option C.

🧠 Memory Trick

"Bank Lends, Borrower Pays."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Financial Mathematics Basics

2 Which of the following analytical statements about repayment is INCORRECT?

A Long-term repayment involves setting aside money periodically.

B EMIs smooth out the repayment burden over the term.

C Failure to repay amortized sequences disrupts the present value balance.

D A loan can be mathematically amortized even if repayment never happens.

💡 Short Explanation

Amortization requires actual repayments. EMIs spread repayment over time. Without repayment, amortization cannot occur.

✅ Correct Answer Explanation

Loan amortization is the systematic repayment of a loan through periodic instalments. Option A is correct because repayments are made periodically. Option B is correct because EMIs distribute repayment evenly. Option C is correct because missed payments disturb the planned amortization schedule and present value calculations. Option D is incorrect because amortization requires actual repayments. Without repayment, the loan cannot be amortized. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Correct because repayment occurs periodically.
Option B: Correct because EMIs distribute repayment over time.
Option C: Correct because missed payments affect the outstanding balance and present value.

🎯 Strategy

used

Elimination

Application:

Recall the definition of loan amortization and eliminate the incorrect statement.

Final Logic:

Amortization requires repayment; therefore Option D.

🧠 Memory Trick

"No EMI = No Amortization."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Loan Amortization

3 Assertion (A):
Principal is the total amount paid at the end of the term.
Reason (R):
Principal includes both the borrowed amount and the total accumulated interest.

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

Principal is the original amount borrowed. Total repayment equals principal plus interest. Both statements are incorrect.

✅ Correct Answer Explanation

The principal is the original amount borrowed from the lender. The total repayment consists of: Total Repayment = Principal + Interest Therefore, the Assertion is false because principal is not the final repayment. the Reason is also false because principal does not include accumulated interest. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Assertion is true.
Incorrect because the assertion is false.
Option C: Both statements are true.
Incorrect because both are false.
Option D: Reason is true.
Incorrect because interest is separate from principal.

🎯 Strategy

used

Elimination

Application:

Differentiate between principal, interest, and total repayment.

Final Logic:

Principal is only the original loan amount; therefore both statements are false and Option A is correct.

🧠 Memory Trick

"Principal First, Interest Extra."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Principal and Interest

4 Assertion (A):
Interest is the price paid by a borrower for the use of the lender's money.
Reason (R):
Interest is always calculated using the flat rate method exclusively for all modern loans.

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

Interest is the cost of borrowing money. Modern loans use different interest calculation methods. Therefore, only the Assertion is true.

✅ Correct Answer Explanation

The Assertion is correct because interest is the amount paid by the borrower to compensate the lender for the use of borrowed funds. The Reason is false because interest is not always calculated using the flat-rate method. Modern financial institutions commonly use the reducing balance (amortization) method, where interest is charged on the outstanding loan balance. Thus, the Assertion is true but the Reason is false. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Both A and R are false.
Incorrect because the assertion correctly defines interest.
Option C: Both A and R are true.
Incorrect because the reason is false.
Option D: A is false, R is true.
Incorrect because the assertion is true while the reason is false.

🎯 Strategy

used

Elimination

Application:

Evaluate the Assertion and Reason separately before checking their relationship.

Final Logic:

Interest is the price of borrowing, but it is not always calculated by the flat-rate method; therefore Option B.

🧠 Memory Trick

"Interest = Cost of Borrowing."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Interest and Loan Methods

5 Assertion (A):
If the rate of interest is 9% compounded monthly, the rate per period (i) is 0.0075.
Reason (R):
The rate per period (i) is calculated by dividing the annual nominal rate by the number of compounding periods per year ((m=12)).

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

Monthly rate equals annual nominal rate divided by 12. (9%=0.09). Therefore, i = 0.09 / 12 = 0.0075

✅ Correct Answer Explanation

Given, Annual nominal rate r = 9% = 0.09 • Monthly compounding m = 12 The periodic rate is i = r / m = 0.09 / 12 = 0.0075 Thus, the Assertion is correct, the Reason correctly explains how the periodic rate is obtained. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Both A and R are false.
Incorrect because both statements are true.
Option B: A is true, R is false.
Incorrect because the reason correctly explains the calculation.
Option D: A is false, R is true.
Incorrect because the assertion is also true.

🎯 Strategy

used

Substitution

Application:

Use the periodic-rate formula directly.

Final Logic:

Since
0.09 / 12 = 0.0075
both statements are true and the Reason explains the Assertion; therefore Option C.

🧠 Memory Trick

"Monthly Rate = Annual Rate ÷ 12."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Periodic Interest Rate

6 Assertion (A):
The term of a loan has no impact on the EMI amount.
Reason (R):
The defined length of time it takes to pay off a loan determines the number of periodic instalments (n), which alters the EMI.

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

Loan term affects the number of EMIs. A longer term generally reduces the EMI. Therefore, only the Reason is true.

✅ Correct Answer Explanation

The Assertion is false because the loan term directly affects the EMI amount. A longer repayment period usually results in a smaller EMI. A shorter repayment period usually results in a larger EMI. The Reason is true because the loan term determines the total number of instalments, n, which is an important variable in EMI calculations. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Both A and R are false.
Incorrect because the reason is true.
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 is false.

🎯 Strategy

used

Elimination

Application:

Recall how the loan tenure influences EMI calculations.

Final Logic:

Loan term changes the number of instalments and therefore changes the EMI; hence Option D.

🧠 Memory Trick

"Longer Loan → Lower EMI."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Loan Tenure and EMI

7 Arrange the order of steps to calculate EMI under the Flat Rate Method:
1. Calculate Total Interest (I)
2. Add Principal and Interest ((P+I))
3. Find Principal (P)
4. Divide by total months (n)

A 3, 1, 2, 4

B 1, 2, 3, 4

C 4, 3, 2, 1

D 3, 2, 1, 4

💡 Short Explanation

First identify the principal. Then calculate total interest. Finally compute the EMI.

✅ Correct Answer Explanation

The Flat Rate EMI is calculated using EMI = (P + I) / n where (P) = Principal, (I) = Total Interest, (n) = Number of monthly instalments. Thus, the correct sequence is: Find the principal ((P)). Calculate total interest ((I)). Add principal and interest ((P+I)). Divide by the total number of months ((n)). Hence, the correct order is 3 → 1 → 2 → 4 Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Begins by calculating interest before identifying the principal.
Option C: Starts with the final computation step.
Option D: Adds principal and interest before calculating the interest.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Arrange the computation steps according to the Flat Rate EMI formula.

Final Logic:

Principal → Interest → Total Repayment → EMI; therefore Option A.

🧠 Memory Trick

"Principal → Interest → Total → EMI."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Flat Rate EMI Calculation

8 Mr. M borrowed from a bank to purchase a house and decided to repay by equated monthly instalments (EMI). Match the loan variables in List I with their calculated numerical values in List II.

List I	List II
1. Total number of instalments (n)	a. ₹89,520
2. Rate of interest per period (i)	b. 180
3. Principal paid during the first year	c. 0.75% per month (0.0075)
4. Interest paid during the first year	d. ₹56,532 (approx.)

A 1-b, 2-c, 3-d, 4-a

B 1-c, 2-b, 3-a, 4-d

C 1-b, 2-a, 3-c, 4-d

D 1-d, 2-c, 3-b, 4-a

💡 Short Explanation

Match each amortization variable with its corresponding value. The intended mapping follows the standard loan calculations. Hence, Option A is correct.

✅ Correct Answer Explanation

For an amortized housing loan: (n) represents the total number of monthly instalments. (i) represents the monthly interest rate. Principal paid during the first year equals the reduction in the loan balance during that year. Interest paid during the first year equals the total EMIs paid minus the principal repaid. Although the numerical entries in List II are omitted, the intended correspondence given in the question is: • (1 → b) • (2 → c) • (3 → d) • (4 → a) Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B
Incorrect because the monthly rate and number of instalments are mismatched.
Option C
Incorrect because the principal and interest values are incorrectly paired.
Option D
Incorrect because several variables are paired with incorrect values.

🎯 Strategy

used

Option Grouping

Application:

Identify the meaning of each amortization variable before matching it.

Final Logic:

The intended mapping corresponds to Option A.

🧠 Memory Trick

"Months → Rate → Principal → Interest."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Loan Amortization Variables

9 Mr. M's loan has an EMI of ₹12,668. In the first year, he paid ₹64,605 towards the principal. What is the interest paid during the first year?
(Total EMIs in a year = \(12\times 12,668=1,52,016\))

A ₹1,52,016

B ₹64,605

C ₹87,411

D ₹10,00,000

💡 Short Explanation

Total annual EMI equals ₹1,52,016. Interest equals total EMI paid minus principal repaid. Hence, the interest paid is ₹87,411.

✅ Correct Answer Explanation

Total EMI paid during the first year: 12 × 12,668 = ₹1,52,016 Interest paid is Interest = Total EMI Paid − Principal Repaid Substituting, Interest = ₹1,52,016 − ₹64,605 = ₹87,411 Therefore, Interest Paid = ₹87,411. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹1,52,016
Incorrect because this is the total EMI paid during the year.
Option B: ₹64,605
Incorrect because this is the principal repaid.
Option D: ₹10,00,000
Incorrect because this is the original loan amount.

🎯 Strategy

used

Substitution

Application:

Subtract the principal repaid from the total annual EMI.

Final Logic:

Since
1,52,016-64,605=87,411,
Option C is correct.

🧠 Memory Trick

"Interest = EMI Paid − Principal Repaid."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: EMI Components

10 If the total EMI paid in a year is ₹1,52,016 and the interest paid is ₹87,411, what is the principal component paid in that year?

A ₹1,52,016

B ₹2,39,427

C ₹87,411

D ₹64,605

💡 Short Explanation

EMI consists of principal and interest. Principal equals total EMI paid minus interest. Therefore, the principal repaid is ₹64,605.

✅ Correct Answer Explanation

The principal component is calculated as Principal Repaid = Total EMI Paid − Interest Paid Substituting the given values, Principal Repaid = ₹1,52,016 − ₹87,411 = ₹64,605 Thus, Principal Component = ₹64,605. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹1,52,016
Incorrect because this is the total EMI paid during the year.
Option B: ₹2,39,427
Incorrect because it exceeds the total annual payment.
Option C: ₹87,411
Incorrect because this is the interest component.

🎯 Strategy

used

Substitution

Application:

Use the relationship:
Principal = Total EMI − Interest

Final Logic:

Since
₹1,52,016 − ₹87,411 = ₹64,605,
Option D is correct.

🧠 Memory Trick

"Principal = EMI − Interest."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: EMI Components

11 Which analytical statement about the Flat Rate Method is INCORRECT?

A It correctly reflects the time value of money by reducing the interest burden as the principal is paid down.

B Each interest charge is calculated based on the original loan amount.

C The total interest is \(P\times r\times n\) where (r) is the annual rate and (n) is the number of years.

D It usually results in a higher effective interest rate than the reducing balance method.

💡 Short Explanation

Flat-rate interest is calculated on the original principal. It ignores the reducing outstanding balance. Therefore, Option A is incorrect.

✅ Correct Answer Explanation

The Flat Rate Method computes interest on the original principal throughout the loan period. Its total interest formula is I = P × r × n Unlike the reducing-balance method, the flat-rate method does not reduce the interest burden as the outstanding principal decreases. Hence, it does not accurately reflect the time value of money. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Correct because flat-rate interest is always calculated on the original principal.
Option C: Correct because this is the standard flat-rate interest formula.
Option D: Correct because the flat-rate method generally results in a higher effective borrowing cost.

🎯 Strategy

used

Elimination

Application:

Recall the defining characteristic of the flat-rate method.

Final Logic:

Flat-rate interest does not reduce with the outstanding balance; therefore Option A.

🧠 Memory Trick

"Flat Rate = Same Interest Base."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Flat Rate Method

12 Evaluate the Reducing Balance Method.
I. Principal outstanding is the present value of remaining payments.
II. Interest is charged only on the unpaid balance.
III. EMI changes every month.

A I, II, and III

B I and II

C II and III

D Only I

💡 Short Explanation

Outstanding principal equals the present value of future EMIs. Interest is charged only on the unpaid balance. EMI normally remains constant throughout the loan.

✅ Correct Answer Explanation

Under the Reducing Balance Method: Statement I is correct because the outstanding principal equals the present value of the remaining instalments. Statement II is correct because interest is calculated only on the outstanding loan balance. Statement III is incorrect because the EMI is generally fixed, while only the principal and interest components vary over time. Therefore, only Statements I and II are correct. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect because Statement III is false.
Option C: Incorrect because Statement I is also correct.
Option D: Incorrect because Statement II is also correct.

🎯 Strategy

used

Elimination

Application:

Recall the basic characteristics of the reducing-balance method.

Final Logic:

Only Statements I and II are true; therefore Option B.

🧠 Memory Trick

"Reducing Balance = Fixed EMI, Reducing Interest."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Reducing Balance Method

13 A person takes a loan of ₹3,00,000 with 7% annual interest for 4 years. Under the flat rate system, the total interest is:

A ₹21,000

B ₹1,00,000

C ₹84,000

D ₹3,84,000

💡 Short Explanation

Use the flat-rate interest formula. Multiply principal, annual rate, and time. The total interest equals ₹84,000.

✅ Correct Answer Explanation

The flat-rate interest is calculated using I = P × r × n where: • P = ₹3,00,000 • r = 7% = 0.07 • n = 4 years Substituting, I = 3,00,000 × 0.07 × 4 = 84,000 Therefore, I = ₹84,000. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹21,000
Incorrect because it represents only one year's interest.
Option B: ₹1,00,000
Incorrect because it exceeds the calculated interest.
Option D: ₹3,84,000
Incorrect because this is close to the total repayment, not the interest.

🎯 Strategy

used

Substitution

Application:

Apply the flat-rate interest formula directly using the given values.

Final Logic:

Since
3,00,000 × 0.07 × 4 = 84,000
Option C is correct.

🧠 Memory Trick

"Flat Interest = Principal × Rate × Time."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Flat Rate Method

14 Using the data from the previous question
\(P=₹3,00,000\)
calculate the EMI under the flat rate method.

A ₹7,000

B ₹6,000

C ₹9,000

D ₹8,000

💡 Short Explanation

Add principal and total interest. Divide by 48 monthly instalments. The EMI equals ₹8,000.

✅ Correct Answer Explanation

Total repayment is P + I = 3,00,000 + 84,000 = 3,84,000 Since the loan period is 4 × 12 = 48 months, the EMI is EMI = 3,84,000 / 48 = 8,000 Thus, EMI = ₹8,000. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹7,000
Incorrect because it is less than the calculated EMI.
Option B: ₹6,000
Incorrect because it underestimates the repayment.
Option C: ₹9,000
Incorrect because it exceeds the calculated EMI.

🎯 Strategy

used

Substitution

Application:

Use the flat-rate EMI formula
EMI = (P + I) / n

Final Logic:

Since
3,84,000 / 48 = 8,000,
Option D is correct.

🧠 Memory Trick

"EMI = Total Repayment ÷ Months."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Flat Rate EMI

15 A couple wishes to purchase a house.
Loan amount
\(P=₹8,00,000\)
Interest = 9% p.a. compounded monthly.
Time = 25 years (300 months).
The present value annuity factor is
The present value annuity factor \(a_{\hat{300}∣0.0075}=119.1616\). Find the EMI \(R\).

A ₹6,713.57

B ₹8,000.00

C ₹10,000.00

D ₹12,140.71

💡 Short Explanation

Use the amortization formula. Divide the loan amount by the annuity factor. The EMI equals ₹6,713.57.

✅ Correct Answer Explanation

For an amortized loan, R = P / a_(300|0.0075) Given, P = ₹8,00,000 and a_(300|0.0075) = 119.1616 Therefore, R = 8,00,000 / 119.1616 ≈ 6,713.57 Thus, R = ₹6,713.57. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹8,000.00
Incorrect because it is higher than the calculated EMI.
Option C: ₹10,000.00
Incorrect because it significantly exceeds the required EMI.
Option D: ₹12,140.71
Incorrect because this is not obtained using the annuity factor.

🎯 Strategy

used

Substitution

Application:

Substitute the loan amount and annuity factor into the amortization formula.

Final Logic:

Since
8,00,000 / 119.1616 ≈ 6,713.57
Option A is correct.

🧠 Memory Trick

"EMI = Loan ÷ Annuity Factor."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Reducing Balance Method

16 Match the following loan scenarios in List I with their correct Equated Monthly Instalment (EMI) in List II.

List I (Loan Scenarios)	List II (Calculated EMI)
1. A loan of ₹2,00,000 at 10% per annum for 5 years, calculated under the Flat Rate system.	a. ₹10,278
2. A loan balance of ₹8,00,000 amortized at 9% per annum compounded monthly for 25 years.	b. ₹7,179
3. A loan of ₹5,00,000 at 8% per annum for 6 years, calculated under the Flat Rate system.	c. ₹5,000
4. A loan of ₹3,00,000 at 7% per annum for 4 years, calculated under the Reducing Balance method.	d. ₹6,713.57 Answer: A

A 1–c, 2–d, 3–a, 4–b

B 1–a, 2–b, 3–c, 4–d

C 1–c, 2–b, 3–a, 4–d

D 1–d, 2–a, 3–b, 4–c

💡 Short Explanation

Match each loan scenario with its calculated EMI. Flat-rate and reducing-balance methods produce different EMIs. The correct matching is Option A.

✅ Correct Answer Explanation

Using the respective EMI calculations: ₹2,00,000 at 10% for 5 years (Flat Rate) → ₹5,000 (c) ₹8,00,000 at 9% compounded monthly for 25 years → ₹6,713.57 (d) ₹5,00,000 at 8% for 6 years (Flat Rate) → ₹10,278 (a) ₹3,00,000 at 7% for 4 years (Reducing Balance) → ₹7,179 (b) Thus, the correct matching is 1 → c 2 → d 3 → a 4 → b Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B
Incorrect because several EMIs are mismatched.
Option C
Incorrect because the second and fourth scenarios are incorrectly paired.
Option D
Incorrect because the flat-rate and reducing-balance EMIs are interchanged.

🎯 Strategy

used

Option Grouping

Application:

Identify the repayment method for each loan and match it with its corresponding EMI.

Final Logic:

Each loan scenario matches only the values given in Option A.

🧠 Memory Trick

"Flat → Formula, Reducing → Annuity."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: EMI Calculation (Flat Rate and Reducing Balance Methods)

17 Mr. M took a loan of ₹10,00,000 (10 years, 9% p.a. compounded monthly). EMI = ₹12,668.
What is the principal left unpaid after one year (present value of remaining 108 payments), given
\(a_{\hat{108}∣0.0075}=73.83916\)?

A ₹10,00,000

B ₹8,47,984

C ₹9,35,395

D ₹64,605

💡 Short Explanation

Outstanding principal equals the present value of remaining EMIs. Multiply the EMI by the annuity factor. The unpaid principal is ₹9,35,395.

✅ Correct Answer Explanation

Outstanding principal after one year is P_outstanding = R × a_(108|0.0075) Substituting, P_outstanding = 12,668 × 73.83916 ≈ 9,35,395 Therefore, P_outstanding = ₹9,35,395. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹10,00,000
Incorrect because part of the principal has already been repaid.
Option B: ₹8,47,984
Incorrect because it is lower than the calculated outstanding balance.
Option D: ₹64,605
Incorrect because this is the principal repaid during the first year, not the remaining balance.

🎯 Strategy

used

Substitution

Application:

Apply the outstanding principal formula using the given EMI and annuity factor.

Final Logic:

Since
Plain text:
12,668 × 73.83916 ≈ 9,35,395
Option C is correct.

🧠 Memory Trick

"Outstanding = EMI × PV Factor."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Outstanding Principal

18 If a loan of ₹8,00,000 is amortized with an EMI of ₹6,713.57 for 300 months, what is the total interest paid?

A ₹8,00,000

B ₹20,14,071

C ₹6,71,357

D ₹12,14,071

💡 Short Explanation

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

✅ Correct Answer Explanation

Total repayment is 300 × 6,713.57 = 20,14,071 Total interest is Interest = 20,14,071 − 8,00,000 = 12,14,071 Therefore, Total Interest = ₹12,14,071. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹8,00,000
Incorrect because this is the principal amount.
Option B: ₹20,14,071
Incorrect because this is the total repayment.
Option C: ₹6,71,357
Incorrect because it is not obtained from the amortization formula.

🎯 Strategy

used

Substitution

Application:

First calculate the total repayment and then subtract the principal.

Final Logic:

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

🧠 Memory Trick

"Interest = Total Paid − Loan."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Total Interest in Amortized Loans

📄 Passage

Mr. M borrowed ₹10,00,000 from a bank to purchase a house and decided to repay by monthly equal instalments in 10 years. The bank charges interest at 9% compounded monthly. The bank calculated his EMI as ₹12,668.

In the given passage, what is the total number of instalments (n) for Mr. M's housing loan?

A 120

B 10

C 108

D 12

💡 Short Explanation

Loan period is 10 years. Each year has 12 monthly instalments. Therefore, the total number of instalments is 120.

✅ Correct Answer Explanation

The loan is to be repaid over 10 years Since EMI is paid monthly, the total number of instalments is n = 10 × 12 = 120 Thus, n = 120. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: 10
Incorrect because this represents years, not monthly instalments.
Option C: 108
Incorrect because this is the number of remaining payments after one year, not the total instalments.
Option D: 12
Incorrect because this represents one year's instalments only.

🎯 Strategy

used

Substitution

Application:

Convert the loan tenure from years into monthly instalments.

Final Logic:

Since
10 × 12=120,
Option A is correct.

🧠 Memory Trick

"Years × 12 = Monthly EMIs."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Loan Tenure

20 Using the passage data, what is the periodic rate of interest (i) per month for Mr. M's housing loan?

A 9%

B 0.75%

C 0.09%

D 1.08%

💡 Short Explanation

Annual nominal rate is 9%. Monthly rate equals annual rate divided by 12. Therefore, the monthly rate is 0.75%.

✅ Correct Answer Explanation

Given the annual nominal interest rate, r = 9% Since interest is compounded monthly, the periodic monthly rate is i = 9% / 12 = 0.75% In decimal form, i = 0.0075 Thus, i = 0.75% per month. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 9%
Incorrect because this is the annual rate, not the monthly rate.
Option C: 0.09%
Incorrect because it is much smaller than the monthly rate.
Option D: 1.08%
Incorrect because it does not equal the annual rate divided by 12.

🎯 Strategy

used

Substitution

Application:

Use the formula
i = r / 12

Final Logic:

Since
9% / 12 = 0.75%,
Option B is correct.

🧠 Memory Trick

"Monthly Rate = Annual Rate ÷ 12."

📚 Class XII – Applied Mathematics – Chapter: Loans and EMI – Topic: Periodic Interest Rate – Page (Reducing Balance Method section)

CUET UG Applied Mathematics Booster Test 3 - Loans, EMI and Loan Amortization

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