The ratio of the principal and the amount after 5 years is 4 : 7. In how many years will the ratio of the principal and simple interest become 5 : 6 at the same rate?

Solution

Solution: Let the principal be 4x and the amount after 5 years be 7x. Interest for 5 years \(=7x-4x=3x\), which is \(\frac34\) of the principal. The annual simple-interest rate is therefore \(\frac{3/4}{5}\times100=15\%\). For the principal-to-interest ratio to be 5:6, interest must equal \(\frac65P\), or 120% of the principal. Time \(=\frac{120}{15}=8\) years. Trick: First calculate the annual simple-interest rate from the first ratio, then calculate the time needed to earn 120% interest.