At simple interest, a man made a deposit of some money in the bank. The amount in his bank account a

With simple interest the amount is A = P + PRT, where P is the money deposited, R is the rate per year and T is the time in years. The interest earned each year is the same amount.

After 10 years the amount is three times the deposit: 3P = P + P × R × 10. Take P from both sides: 2P = 10PR, so R = 2/10 = 0.2, that is 20% per year.

Now find the time for the amount to be five times the deposit: 5P = P + P × 0.2 × T. That gives 4P = 0.2PT, so T = 4 ÷ 0.2 = 20 years.

A quick way to see it: it takes 10 years to earn 2P in interest, so the money grows by P every 5 years. To reach 5P the account must earn 4P of interest, and 4 × 5 = 20 years.