Question

Following her 18th birthday, Madison began investing $24 at the end of each week in an account earning 7% per year compounded weekly. She plans to continue making weekly investments until she turns 68. If she had waited until she turned 47, how much would she have to invest weekly in order to have the same retirement nest egg at age 68? Round to the nearest cent. (Hint: Find the size of the retirement nest egg, then use that to solve for CF under the shorter investment scenario)

Answer 1

The answer is $26.80.

Step-by-step explanation:

*Some inputs for the calculation as below:

One year period has 52 weeks

=> At the time she turns 68, she will have: (68-18) x 52 = 2,600 equal weekly cash flows; At the time she turns 47, she will have: (47-18) x 52 = 1,508 equal weekly cash flows.

* Present value of the investment plan lasting until she turns 68:

[ 24 / (7%:52) ] x [ 1 - (1+ (7%/52)^(-2,600) ] = $17,289.

* To have the same retirement nest egg at age 68, the present value of the investment plan lasting until she turns 47 should be equal to $17,289. Denote x is the weekly investment under the shorter investment scenario, we have:

[x / (7%:52) ] x [ 1 - (1+ (7%/52)^(-1,508) ] = $17,289 <=> x = $26.80.