Question

A man borrowed some amount at 12.5% compound interest compounded semi-annually. He borrowed rs. 500 more at the end of 6th month. The amount compounded at the end of the year is rs. 4482.42. Find the sum borrowed at the start of the year.

Answer 1

Answer:

rs. 3500

Step-by-step explanation:

The amount A after compounding at rate r per compounding period for n compounding periods, starting with principal P, is

A = (1+r)ⁿP

We have rate 12.5% per annum (I presume).  As the compounding period is 6 months, the rate per compounding period is

r = 12.5% / 2 = 6.25% = 0.0625

The rs. 500 compounds for 1 period, so it becomes

(1+r)¹ × 500 = 1.0625 × 500 = 531.25

So the remaining A = 4482.42 - 531.25 = 3951.17 is due to the principal P that was borrowed at the beginning of the year.  Since it has grown for 2 compounding periods, the formula gives

3951.17 = 1.0625² × P

=> P = 3951.17 / 1.0625² = 3500