Problem
Peter is 25 years old and is planning for his pension. He intends to retire in forty years' time, when he is 65. First, he calculates how much he wants to have in his pension fund when he retires. Then, he calculates how much he needs to invest in order to achieve this. He assumes that, in the long run, money can be invested at an inflation-adjusted annual rate of 3% compounded annually.
A. Peter wants to have a fund that could, from the date of his retirement, give him a payment of €20,000 at the start of each year for 25 years. Calculate the value of the fund required on the date of retirement.
B. Peter plans to invest a fixed amount of money every month in order to generate the fund calculated in part A). Find, corrected to four digits, the rate of interest per month that would, if paid and compounded monthly, be equivalent to an effective annual rate of 3%.
C. If Peter makes 480 equal monthly payments of €X from now until his retirement, what value of X will give the fund he requires?