Ramesh borrowed some money and agreed to pay-off by paying Rs. 4,565 at the end of the first year and Rs. 6,534 at the end of the second year. If the rate of compound interest is 10% per annum, find the amount borrowed by Ramesh.

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 17 Jan 2023 Shift 4)

Answer 1

Given:

Ramesh pays Rs. 4,565 at the end of the first year

and Rs. 6,534 at the end of the second year.

Rate of compound interest = 10% p.a.

Concept:

Compound Interest formula A = P (1 + r/n)^(nt)

Solution:

For the first year,

Amount (A1) = Principal (P1) × (1 + r/n)^(nt)

⇒ P1 = A1 / (1 + r/n)^(nt)

⇒ P1 = 4565 / (1 + 0.1/1)^(1×1)

⇒ P1 = 4565 / 1.1

⇒ P1 = 4150

⇒ For the second year, Amount (A) = Principal (P2) × (1 + r/n)^(nt)

⇒ P2 = A2 / (1 + r/n)^(nt)

⇒ P2 = 6534 / (1 + 0.1/1)^(1×2)

⇒ P2 = 6534 / 1.21

⇒ P2 = 5400

Total amount borrowed by Ramesh = P1 + P2

⇒ Total amount = 4150 + 5400

⇒ Total amount = Rs. 9550

Therefore, the amount borrowed by Ramesh is Rs. 9550.