Question

I have this question for homework in finance, but I cannot figure out which formula to use or how to begin to solve it.

Following her 18th birthday, Madison began investing $22 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 46, 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

Number of years = 68 - 22 = 46

Assuming there are 52 weeks in a year.

Number of periods = 46 * 52 = 2,392

Rate = 7% / 52 = 0.1346%

Future value at age 68 = annuity * [(1 + r)ⁿ - 1] / r

Future value at age 68 = 22 * [(1 + 0.001346)²³⁹² - 1] / 0.001346

Future value at age 68 = 22 * 17,804.46317

Future value at age 68 = $391,698.1897

If he waited till age 46:

Number of years = 68 - 46 = 22

Number of periods = 22 * 52 = 1,144

Future value at age 68 = annuity * [(1 + r)ⁿ - 1] / r

391,698.1897 = annuity * [(1 + 0.001346)^1,144 - 1] / 0.001346

391,698.1897 = annuity * 2,718.382716

annuity = 144.09

He will need to invest weekly $144.09