Question

A certain sum of money amounts to Rs 2646 in 2 years and to Rs 2778 in 3 years at the same annual compound interest rate. Find the rate of interest and the sum

Answer 1

Answer:

Step-by-step explanation:

Answer 2

i) A certain sum of money amounts to Rs 2646 in 2 years

(ii) It then amounts to Rs 2778.30 in 3 years

To find:

(I) Rate of interest and sum.

Solution:

The amount (A) in compound interest is given as:

A = P(1 + r/n)^(nt)

Since interest is compounded annually, n=1.

For first case, A = Rs 2646, t = 2.

2646 = P(1 + r)^2 ...(1)

For second case,

A = Rs 2778.30, t = 3.

2778.30 = P(1 + r)^3 ...(2)

Dividing (2) by (1), we get,

(2778.30/2646) = (1+r)

=> 1 + r = 21/20

=> r = 1/20

=> r = (100/20)% = 5%

So, rate = 5% p.a.

P(1 + 1/20)^2 = 2646

=> 441P/400 = 2646

=> P = Rs 2400

So, sum is Rs 2400 and rate of interest is 5% p.a.