Question

Following her 18th birthday, Madison began investing $41 at the end of each week in an account earning 5% per year. She plans to continue making weekly investments until she turns 68. If she hadn't started investing until she turned 56, how much would she have to invest each week 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 under the first long horizon scenario, then use that number to solve for CF under the short investment horizon scenario.]

Answer 1

Calculation of size of retirement nest egg:

Rate = 5% / 52
Nper = (68 - 18) * 52 = 2600
PMT = $41
PV = 0

Size of retirement nest egg can be calculated by using the following excel formula:
=FV(rate,nper,pmt,pv)
=FV(5%/52,2600,-41,0)
= $476,197.96

Size of retirement nest egg = $476,197.96

Calculation of amount of weekly investment:

Rate = 5% / 52
Nper = (68 - 56) * 52 = 624
FV = 476,197.96
PV = 0

Weekly investment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(5%/52,624,0,-476197.96)
= $557.31

Amount of weekly investment = $557.31