Question

A certain sum sf money amount to rs 7028 in 3 years and rs 8456 in 5 years . find the sum and the re rate of interest.​

Answer 1

Answer:

Sum is Rs.5325 and rate of interest is 9.7 per cent per year

(Both figures are rounded off)

Step-by-step explanation:

We are assuming that this is a case of compound interest.

P = initial amount in Rs.

R = rate of interest per cent per year

T = number of years

A = final amount at the end of T years

A = P(1 + R/100)^T

Now:

When T = 3, A = 7028

=> 7028 = P(1 + R/100)^3 ..........(i)

When T = 5, A = 8456

=> 8456 = P(1 + R/100)^5 .....(ii)

Dividing (ii) by (i), we get:

(8456/7028) = (1 + R/100)^2

=> 1.203187 = (1 + R/100)^2

=> (1 + R/100) = $\sqrt{1.203187}$

=> (1 + R/100) = 1.097   (approx)

=> R/100 = 1.097 - 1

=> R/100 = 0.097

=> R = 9.7

The rate of interest (R) is 9.7 per cent per year

To find the sum, we use eqn (i) or (ii)

Using (i), we get:

7028 = P(1 + (9.7/100))^3

=> 7028 = P(1.097)^3

=> 7028 = P(1.3198)

=> P = 7028/1.3198

=> P = 5325 (approx)

The sum (P) is Rs.5325