Question

A sum of money invest at compound interest which amounts to Rs. 1500 in 3 years and Rs. 1650 in four years. Find the rate of interest.
1. 10%
2. 5%
3. 15%
4. 7%

Answer 1

Correct Answer - Option 1 : 10%

Given

Amount in 4 years = Rs. 1650

Amount in 3 years = Rs. 1500

Formula used

A = P(1 + r%)^t

Where A, P, r and t are amount, principal, rate and time respectively

Calculation

1650 = P(1 + r%)⁴

1650/(1 + r%)⁴ = P.     ----(1)

1500 = P(1 + r%)³

1500/(1 + r%)³ = P.     ----(2)

From (1) and (2)

1650/(1 + r%)⁴ = 1500/(1 + r%)³

⇒ 1650/1500 = (1 + r%)⁴/(1 + r%)³

⇒ 1650/[1 + r%]⁴ = 1500/[1 + r%]³

⇒ 1650/1500 = (1 + r%)⁴/(1 + r%)³

⇒ 1650/1500 = (1 + r%)

⇒ (1650 × 100)/1500 = 100 + r

⇒ 110 - 100 = r

⇒ 10% = r

∴ Rate is 10% per annum