Soumya and Mangal, both took a loan of Rs.4000 from a bank, at the sam

1.	Soumya and Mangal, both took a loan of Rs.4000 from a bank, at the same time. Both needed to repay the loan after a time period of 2 years, compounded at a rate of 15% quarterly for Soumya, while compounded annually at a rate of 20% for Mangal. Find the difference (in Rs.) in the amount needed to be repaid by Soumya and Mangal, at the end of two years.1. 390.122. 290.423. 300.54. 350.425. 420.52
Answer» Correct Answer - Option 1 : 390.12 Given: Loan taken from the bank by Soumya and Mangal, each = Rs.4000 The time period to repay the loan for both = 2 years Rate of Interest Compounded Quarterly for Soumya = 15% Rate of Interest Compounded Annually for Mangal = 20% Formulae Used: If P = Principal, R= Rate of Interest, and n = number of years, then: When the interest is compounded annually, Amount = P [1 + (R/100)]ⁿ When the interest is compounded quarterly, Amount = P [1 + (0.25R/100)]4n Calculation: The amount needed to be repaid by Soumya at the end of two years is given by: 4000 × {1 + [(0.25 × 15)/100]}⁸= 4000 × [1 + (3.75/100)]8 ⇒ 4000 × (1.0375)8 = Rs.5369.88 The amount needed to be repaid by Mangal at the end of two years is given by: 4000 × [1 + (20/100)]² = 4000 × (1.2)² ⇒ 4000 × 1.44= Rs.5760 ∴ The difference in the amount to be repaid by Soumya and Mangal at the end of two years is given by: 5760 - 5369.88 = 390.12 ∴ The difference in the amount needed to be repaid by Soumya and Mangal after two years is Rs.390.12

Soumya and Mangal, both took a loan of Rs.4000 from a bank, at the same time. Both needed to repay the loan after a time period of 2 years, compounded at a rate of 15% quarterly for Soumya, while compounded annually at a rate of 20% for Mangal. Find the difference (in Rs.) in the amount needed to be repaid by Soumya and Mangal, at the end of two years.1. 390.122. 290.423. 300.54. 350.425. 420.52

Answer» Correct Answer - Option 1 : 390.12

Given:

Loan taken from the bank by Soumya and Mangal, each = Rs.4000

The time period to repay the loan for both = 2 years

Rate of Interest Compounded Quarterly for Soumya = 15%

Rate of Interest Compounded Annually for Mangal = 20%

Formulae Used:

If P = Principal,

R= Rate of Interest, and

n = number of years, then:

When the interest is compounded annually,

Amount = P [1 + (R/100)]ⁿ

When the interest is compounded quarterly,

Amount = P [1 + (0.25R/100)]4n

Calculation:

The amount needed to be repaid by Soumya at the end of two years is given by:

4000 × {1 + [(0.25 × 15)/100]}⁸= 4000 × [1 + (3.75/100)]8

⇒ 4000 × (1.0375)8 = Rs.5369.88

The amount needed to be repaid by Mangal at the end of two years is given by:

4000 × [1 + (20/100)]² = 4000 × (1.2)²

⇒ 4000 × 1.44= Rs.5760

∴ The difference in the amount to be repaid by Soumya and Mangal at the end of two years is given by:

5760 - 5369.88 = 390.12

∴ The difference in the amount needed to be repaid by Soumya and Mangal after two years is Rs.390.12