Solve the problem.

Question

The actual phrasing: Assume the cost of a gallon of milk is $2.50. With continuous compounding, find the time it would take the cost to be 3 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

Answer 1

We want to know when the growth rate reaches 3, so we have to work out n where 1.06ⁿ=3.

Taking logs we have nlog1.06=log3 using any base for the logs. So n=log3/log1.06=18.85 years.

If we round this up to one decimal place we get 18.9 years.