Question

A sum of money if invested at ci for 2 years amounts to 57600 and 65536 in 4 years. Find the rate and the sum

Answer 1

Answer:

Rate = 6.66%

Sum = 50625

Explanation:

Let P be the sum of money invested

Compound Interest Cases:

Case 1 (Investment for 2 years):

57600 = P*[1+(r/100)]^2

Case 2 (Investment for 4 years):

65536 = P*[1+(r/100)]^4

Dividing Case 1 by Case 2

57600/65536 = 1/[1+(r/100)]^2.....(3)

Taking square root of both sides for (3),

240/256 = 1/[1+(r/100)]

Taking reciprocal of both sides,

256/240 = 1 + r/100

16/15 = 1 + r/100

r = 6.66%

Putting the Value of r in Case 1:

57600 = P*[1+(6.66/100)]^2

57600 = P*(1.0666^2)

P = 57600/(1.0666^2)

Hence, P = 50625