Question

If Rs 40000 amounts to Rs 46305 in $1\frac{1}{2}$ years, compound interest payable half-yearly, find the rate of interest per annum.

Answer 1

Given

Principal (P) = Rs 40000

Amount (A) = Rs 46305

Period (n) = $1\frac{1}{2}$years = 3/2 years

So half yearly, 2n = 2 × (3/2) = 3 years.

Let the rate of interest be r% p.a.

A / P = (1 + r / 100)${}^n$

46305 / 40000 = (1 + r / 100)${}^3$

(1 + r / 100)${}^3$ = 46305 / 40000

On further calculation, we get,

(1 + r / 100)${}^3$ = 9261 / 8000

(1 + r / 100)${}^3$ = (21 / 20)${}^3$

We get,

(1 + r / 100) = (21 / 20)

r / 100 = (21 / 20) – 1

r / 100 = 1 / 20

r = 100 / 20

We get,

r = 5

Therefore, rate of interest = 5% for half year.

So, 2 × 5 = 10% per annum.