Two friends Julie and William invest equal sums of money at a certain rate of interest. While Julie’s investment is through a simple interest instrument, William invests on a compound interest instrument. At the end of year 2 the interest earned by William is Rs.225 more than Julie and at the end of year 3, the gap widens to Rs.708.75. What was the principal that each of them invested and at what rate of interest?

Explanation:

If we do this problem using Pascal’s triangle we can solve easily.

At the end of 2 years, CI = 2 SI + II, SI = 2 SI where II = Interest on Interest

At the end of 3 years, CI = 3 SI + 3 II + Ill, SI = 3 SI where Ill = Interest on Interest on Interest

Difference = 3II + Ill = 708.75

or lll = 708.75−3×225=33.75

Rate of interest = III\II×100=33.75\225×100 = 15%

The difference at the end of two years is Rs.225 which is the interest on interest at the rate of

15% per annum.

Therefore, the simple interest during year 1 = 225\15×100 = Rs.1500. As the simple interest is Rs.1500 per year and the rate of interest is 15%, the principal invested = 1500\15×100 = Rs.10,000