# Solved Example #14

Wednesday, January 22nd, 2014

Question : A person lent out some money for 1year at 6% per annum simple interest and after 18 months he again lent out the same money at a simple interest of 24% per annum. In both cases he got Rs.4704. What was the amount that he lent out if interest is paid half yearly?

a. Rs 4000

b. Rs 4200

c. Rs 4400

d. Rs 3600

In the first case, the rate of interest is 3% per half-year. The money will become

1.03x after 6 months from t = 0

1.06x after 12 months from t = 0

1.09x after 18 months from t = 0

1.12x after 24 months from t = 0 and so on ….

In the second case, the rate of interest is 12% per half-year. The money is given out at t = 18.

The money will become:

1.12x after 6 months from t = 18, which is 24 months from t = 0.

So after 2 years the returns from both the investments will be same. They will be 1.12x

This was the point at which he gets back 4704 Rs.

=> 1.12x = 4704

=> x = 4200 Rs.

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