Arun and Gaurav have to clear their respective loans by paying 3 equal annual instalments of Rs. 30,000 each. Arun pays @ 10% per annum of simple interest while Gaurav pays 10% per annum compound interest. What is the difference in their loan amounts?a)Rs. 400b)Rs. 350c)Rs. 300d)Rs. 450e)Rs. 500Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:

Arun and Gaurav have to clear their respective loans by paying 3 equal annual installments of Rs. 30,000 each.
Arun pays @ 10% per annum of simple interest.
Gaurav pays 10% per annum compound interest.

To find:

The difference in their loan amounts.

Solution:

Let's first calculate the loan amount for both Arun and Gaurav.

Arun:

Arun is paying the loan amount with simple interest.

Simple Interest (S.I.) formula: S.I. = (Principal * Rate * Time) / 100

Given that Arun pays 3 equal annual installments of Rs. 30,000 each, we can calculate the principal amount using the formula:

Principal = (Installment * 100) / (Rate * Time)
Principal = (30000 * 100) / (10 * 3)
Principal = Rs. 100,000

Gaurav:

Gaurav is paying the loan amount with compound interest.

Compound Interest (C.I.) formula: C.I. = P(1 + R/100)^n - P

Given that Gaurav pays 3 equal annual installments of Rs. 30,000 each, we can calculate the principal amount using the formula:

Principal = (Installment * (1 + Rate/100)^Time - Installment) / (Rate/100)
Principal = (30000 * (1 + 10/100)^3 - 30000) / (10/100)
Principal = Rs. 93,930.23 (approx.)

Difference:

Now, we can find the difference in their loan amounts.

Difference = Principal(Arun) - Principal(Gaurav)
Difference = Rs. 100,000 - Rs. 93,930.23
Difference = Rs. 6,069.77 (approx.)

Therefore, the difference in their loan amounts is Rs. 6,069.77, which can be approximated as Rs. 6,000.

Therefore, the correct answer is option C) Rs. 300.

Answer

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