Question

A sum of $7000 amounts to 8260 in 3 years at a certain rate of interest. In what time will
5000 amount to 6500 at the same rate of interest?​

Answer 1

If we consider it is a case of simple interest then

Interest for 3 years = 8260 - 7000 = 1260

Interest for 1 year = 1260/3 = 420

Rate if interest = (420/7000) * 100 = 6%

For Rs. 5000 becomes Rs. 6500,

the interest = 6500 - 5000 = 1500

The rate is 6%

Yearly interest = 5000 * 6/100 = 300

No. of years = 1500/300 = 5 Ans

For compound interest, let the rate is r

7000 * ( 1 + r/100)^3 = 8260

Or, (1 + r/100)^3 = 8260/7000 = 1.18

Or, 1 + r/100 = 1.18^(1/3) = 1.05672

Or, r = (1.05672 - 1) * 100 = 5.672%

For Rs. 5000 becoming Rs. 6500, let the number of years = x

So, 5000 * (1.05672)^x = 6500

Or, (1.05672)^x = 6500/5000 = 1.3

Taking log and solving, x log 1.05672 = log 1.3

Or x = log 1.3 / log 1.05672 = 0.1139/0.02396

Or x = 4.75 years Ans.