In what time will ₹6,750 amount to ₹8,984.25 at the interest rate of 20% per annum, compounded half-yearly?

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 31 Jan 2023 Shift 3)

Answer 1

Given:

Principal = ₹6,750,

Amount = ₹8,984.25,

Rate of interest = 20% per annum

Compounded half yearly

Concept:

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

Calculation:

Since interest is compounded half-yearly,

n = 2 and r = 20% = 0.20 becomes 0.20/2 = 0.10 per half-year.

Substitute the given values into the formula and solve for t.

⇒ 8984.25 = 6750 × (1 + 0.10)^(2t)

⇒ 1.331 = (1.10)^(2t)

To get 2t, we need to find how many times we need to multiply 1.10 by itself to get 1.331.

⇒ 2t ≈ 3

⇒ t = 3 ÷ 2 = 1.5 years

Therefore, the time required is approximately 1.5 years