A sum of money becomes two times of itself in 8 years at simple interest, and it becomes four times of itself in 2 years at compound interest, when interest is compounded annually. Find the ratio of the rate of simple interest to the rate of compound interest offered per year.

1 : 8

A sum of money becomes two times of itself in 8 years at simple interest

Simple interest = \(\frac{P × R × T}{100}\)

P + \(\frac{P × R × 8}{100}\) = 2P

\(\frac{1 × R × 8}{100}\) = 1

R = 12.5%

A sum of money becomes four times of itself in 2 years at compound interest

4P = P [ 1 + \(\frac{R}{100}\) ]² 

2 = [ 1 + \(\frac{R}{100}\) ]

\(\frac{R}{100}\) = 1

R = 100%

Now,

Ratio of rate of simple interest to compound interest

12.5  :  100

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