A sum becomes 27 times in 3 years, compounded annually at a certain rate of interest. Calculate annual interest rate.

Gi​ven:

Amount = 27 P in 3 years

Concept:

In compound interest, the ratio of the amount and the principal is given by:

\(\frac{A}{P} = (1 + \frac{R}{100})^n\)

Calculation:

We know that,

\(\frac{A}{P} = (1 + \frac{R}{100})^n\)

\(⇒ \frac{27}{1} = (1 + \frac{R}{100})^3 \)

\(⇒ 3^3 = (1 + \frac{R}{100})^3 \)

\(⇒ 3 = (1 + \frac{R}{100}) \)

⇒ R/100 = 3 - 1 = 2

⇒ R = 200%

Hence, the annual interest rate is 200%.

Shortcut Trick

A sum becomes 27 times in 3 years

3^x = 27

⇒ 3^x = 3³

⇒ x = 3

Rate = (x - 1) × 100%

⇒ (3 - 1) × 100% = 200%

∴ The annual interest rate is 200%.