A sum of money becomes 1.6 of itself in 5 yrs at a certain rate of SI. Find the rate of interest?

If you invest a principle p at an interest rate of i then at the end of the first period you have T = p x (1 + i). After two periods you have T = p x (1 + i)^2 and after N periods you have T = p x (1 + i)^N.

You are given N=5 and T = 1.6

IOW the problem is 1.6 = (1 + i)^5 and we use logarithms to solve it.

log(1.6) = 5log(1 + i)

0.204119983 = 5log(1 + i)

0.040823997 = log(1 + i) Now antilog. (That means 10 to that power.)

1.09856 = 1 + i

i = 9.856%

Check: 1.09586^5 = 1.6