Question

The difference between the compound interest and the simple interest on a certain principal for 2 years at the rate of 4% per annum is ` 150. Find the principal.

Answer 1

Given:

Difference between simple interest and compound interest  = Rs.  150

rate (r) = 4% per annum

time (n) = 2 years

To find:

Principal amount

Solution:

Let the principle amount be x

Then,

S.I. = x * 4 * 2 / 100

=> S.I. = 2x / 25

Now , in compound interest

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

A = P(1 + 4/100)^2

=> A = 676x / 625

Now , C.I. = A - P

=> C.I. = (676x / 625) - x

=> C.I. = 51x / 625

According to the question, we have

C.I. - S.I. = 150

=> (51x / 625) - (2x/25) = 150

=> (51x - 50x)/625 = 150

=> x/625 = 150

=> x = 150 * 625

=> x = 93750

Hence, the required principal amount is Rs. 93750.