Question

G and L will be retiring in four years and would like to buy a retirement house. They estimate that they will need $550,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 8% on their money, compounded annually, over the next four years, how much must they invest at the end of each year for the next four years to have accumulated $550,000 by retirement?

Answer 1

Hopefully, the problem is worded as follows:

a after 3 years = A (1.08)^3 = 1.2597 A after 3 years (invested at end of year)

a after 2 years = A (1.08)^2 = 1.1664 A after 2 years

a after 1 year = A (1.08) = 1.08 A

a last year = A

adding the columns

4 a = 4.5061 A where A is the amount invested each year and a is the total worth of such an investment

or a = 1.12653 A

A = a / 1.12653 = 550,000 / 1.12653 = 488,226 for the total investment

Each year 488,226 / 4 must be invested = 122,057