A certain sum amounts to Rs. 7,200 in 2 years at 6% per annum compound interest, compounded annually. Find the sum (in Rs., to the nearest integer).

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 08 Feb 2023 Shift 1)

Answer 1

Data:

Amount after 2 years (A) = ₹7200

Annual interest rate (r) = 6%

Time (t) = 2 years

Concept:

For compound interest compounded annually,

A = P(1 + r/100)^t. We can rearrange this to solve for P.

Solution:

Convert the annual interest rate from a percentage to a decimal

⇒ r = 6/100 = 0.06

The problem states that the interest is compounded annually, so n = 1

Substitute A, r, n, and t into the compound interest formula and solve for P

⇒ 7200 = P(1 + 0.06/1)^(1×2)

⇒ 7200 = P(1 + 0.06)²

⇒ 7200 = P(1.06)²

⇒ 7200 = P(1.1236)

Solve for P

⇒ P = 7200 / 1.1236

⇒ P = 6408.35

Therefore, the initial sum (rounded to the nearest integer) is Rs. 6408.