Question

Your friend Ellen is celebrating her 25th birthday (i.e., she is 25 today) and wants to start saving for her anticipated retirement at age 55. She wants to be able to withdraw $10,000 from her savings account on each birthday for 10 years following her retirement (the first withdrawal will be on her 56th birthday). Ellen intends to invest her money in the local saving bank, which offers 8% (EAR) interest per year.

Suppose Ellen wants to make 24 deposits with the same amount C to cover her retirement needs. She plans to start making these deposits on her 26th birthday and continues to make deposits on every birthday until she is 50 (the last deposit will be on her 50th birthday). The only exception is she will skip the deposits on her 40th birthday as she will spend the money to travel in Europe. What is the minimal amount of C will Ellen have to deposit?

Answer 1

Ellen will invest for 30years and withdraw $10,000 for ten years

At Ellen's 55th Birthday, the present value of withdrawals = $10,000 * CPVF (8%, 10years)

= $10,000 * 6.710

=$67,100

So, at Ellen's 55th birthday the accumuation should be $67,100

Let the annual deposit be C

at Ellen's 50th bithday, Accumulating factor (8%, 25 years) = 73.1059

but Ellen missed the 40th deposit

So the Ellen's factor will be 73.1059 - 1.08^10

= 73.1059 - 2.15892

= 70.94698

At 55th birthday = 70.94698*1.08^5

= 70.94698 * 1.469

=104.22

Annual Deposit = $67,100 / 104.22

Annual Deposit = $643.82