Question

Ashley invests a certain amount at compound interest. He receives Rs. 6048 at end of the second year and Rs. 7257.6 at end of the third year, what would he have received at end of two years if the rate of percentage decreased to 10%?
1. Rs. 5272
2. Rs. 4674
3. Rs. 4580
4. Rs. 5082

Answer 1

Correct Answer - Option 4 : Rs. 5082

Given:

A = Rs. 6048 (after 2 years)

A = Rs. 7257.6 (After 3 years)

Formula used:

A = P × {1 + (R/100)}^N

Where, P = Principal, R = Rate of interest, N = Number of years

Calculation:

Let Amount after 3 years and 2 years be A3/A2 respectively.

Here, A₃/A₂ = 7257.6/6048

⇒ 7257.6/6048 = 1.20

A3/A2 = [P{1 + (R/100)}3]/[P{1 + (R/100)}2]

⇒ 1.20 = {1 + (R/100)}

⇒ 0.20 = R/100

⇒ R = 20%

Now, calculating P,

⇒ 6048 = P × {1 + (20/100)}²

⇒ 6048 = (P × 6 × 6)/(5 × 5)

⇒ P = Rs. 4200

∵ R decreased to 10%,

⇒ New rate of interest is (20 – 10) = 10%

A = 4200 × {1 + (10/100)}²

⇒ A = (4200 × 11 × 11)/(10 × 10)

⇒ A = 5082

∴ He will receive Rs. 5082 at the end of two years if the rate of percentage decreases by 10%.