Question

UI Meest. Calculate the sum of money lent out.
34 A sum of money amounts to 313230 in one year and to 513891-50 in 15 years at
compound interest, compounded semi-annually. Find the sum and the rate of interest
per annum​

Answer 1

Answer:

Given  

A sum of money amounts to Rs.13230 in one year and to Rs.13891.50 in 3/2 years at compound interest, compounded semi-annually. Find the sum and the  rate of interest per annum ?​

Let r be rate of interest and p be the sum. Given S1 = 13230 and S2 = 13891.5

Rate of interest half yearly = r/2

Conversions will be 2 and 3 respectively.

Time n1 = 2 , n2 = 3

We know that

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

13230 = P(1 + r/2/100)^2

13230 = P(1 + r/200)^2-----------1

13891.5 =P(1 + r/200)^3---------2

Now dividing equation 2/1 we get

13891.5/13230 = [P(1 + r/200)^3] / [P(1 + r/200)]^2

1 + r/200 = 13891.5 / 13230

1 + r/200 = 1.05

r/200 = 1.05 – 1

r/200 = 0.05

r/200 = 5/100

r/2 = 5

r = 10

Now rate of interest is 10%

From equation 1 we get

13230 = P(1 + 10/200)^2

13230 = P(1 + 1/20)^2

13230 = P(21/20)^2

13230 = 441 P / 400

441 P = 13230 x 400

P = 13230 x 400 / 441

P = 12,000

So sum will be Rs 12,000