Question

Ben wants to pay $25,000 in cash to buy his father’s Mercedes when the lease is up in three years. Ben gets paid every two weeks (26 times per year) and wants to put aside equal amounts from each paycheck so that he has $25,000 after three years. To find out how much to put aside, he calculated the present value of $25,000 using a 6% rate, then divided by 26 to get the bi-weekly payment. Will this approach give ben $25,000 in three years? Explain your answer. (6 points)

Answer 1

The approched used by Ben to calculate biweekly payment is wrong by calculating PV of $25000 because Ben is not putting aside whole money together and he also neglected that each payment would be compounded for different periods. So correct amount is calculated below

Given

Target Amount T=$25000

Number of payments in a year= 26

so for three years number of payments N=26*3=78

R=6%

r=6%/26=0.23%

Let A be the payment per biweekly

So A = T*r/((1+r)^N-1)

A=$292.90