Question

The difference between simple interest and compound interest for a certain sum of money at 8% p.a. for one and a half year, when interest is compounded half yearly is Rs. 228. Find the sum.

Answer 1

Sol:
Let the principal be Rs 'P'
Time = 1 1/2 year = 3/2 years
Rate of interest = 8 %

(i)
Simple interest = (P x T x R) / 100
                      = (P x 3 x 8) / (2 x 100)
                      = 3P / 25
(ii)
Amount at the rate of compound interest = P(1 + r/100)n
= P(1 + 8/100)3
= P(27/25)3
= 19058P / 15625

Compound Interest = (19058P / 15625) - P
                               = 3433 P / 15625

Difference between the compound and simple interests = Rs 228

(3433 P / 15625) - (3P / 25) = 228
(3433 P / 15625) - (1875P / 15625) = 228

(1558 P / 15625) = 228

P = 2286.56

Therefore, the sum lent is Rs  2286.56