Question

Rakesh borrowed ₹ 60,000 at 12% per annum compound interest. If he pays 50% of the sum borrowed at the end of the first year and 50% of the remaining loan at the end of the second year, then find the amount of loan outstanding at the beginning of the third year.

• A. ₹ 20,664
• B. ₹ 20,832
• C. ₹ 26,664
• D. ₹ 24,664

Answer 1

The correct option is C

₹ 26,664

Given, P = ₹ 60,000 and R = 12

For the first year:

I = $\frac{PTR}{100}$

= $\frac{60,000\times 1\times 12}{100}$

= ₹ 7200

Given that he pays off 50% of the amount borrowed.
Hence amount paid back by him
= 50% of 60,000
= ₹ 30,000

For the second year:

Principal = ₹ 30,000 + 7200

= ₹ 37,200

I = $\frac{PTR}{100}$

= $\frac{37200\times 1\times 12}{100}$

= ₹ 4464

Actual amount due at the beginning of the third year
= ₹ 37,200 + ₹ 4,464
= ₹ 41,664

Given that he pays off 50% of the remaining borrowed sum.
50 % of 30,000 = ₹ 15,000

Hence the total amount due at the beginning of the third year
= ₹ 41,664 - 15,000
= ₹ 26,664