Question

the ratio of interest between the compound and simple interest for two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?

Answer 1

Simple interest after two years is $P*2R$ ,

after three years $P*3R$ , where P is the sum of money, R - interest rate.

Compound interest after two years is $P*(1+R)^2-P$

after three years $P*(1+R)^3-P$

Difference between compound and simple interest on certain sum of money after two years is:

$P*(1+R)^2-P-P*2R=P*R^2$

Difference between compound and simple interest on certain sum of money after three years is:

$P*(1+R)^3-P-P*3R=3P*R^2+P*R^3$

Therefore, the ratio would be:

$\frac{P*R^2}{3P*R^2+P*R^3} = \frac{11}{37}$

By solving this equation we get rate of interest:

$R=\frac{4}{11}\approx36.36$ %