Question

A young graduate is planning on saving $745.00 each quarter for four years in an investment account paying 15.96% interest that is compounded quarterly. His first deposit will be made at the end of the next quarter, so this is a regular annuity. The balance from this investment account will be used as a down payment on a new car. Also, in 4 years, he also plans on being able to afford a 60-month car loan with $317.00 monthly payments at a 13.32% APR interest rate. Given the graduate’s plans, how expensive of a “dream car” will he expect to be able to purchase in four years?

Answer 1

- Periodic quarterly savings for four years = $745 each quarter

Calculating the Future Value at the end of Year 4:-

Where, C= Periodic Payments = $745

r = Periodic Interest rate = 15.96%/4= 3.99%

n= no of periods = 4 years*4 = 16

Future Value = $16,246.26

So, accumulated value at the end of year 4 which is used as down-payment is $16,246.26

After 4 years, you will also take a loan for car for which you can afford to pay $317 monthly payment for 60 months.

Calculating the Present Value of these paymnets or the loan amount:-

Where, C= Monthly Payments = $317

r = Periodic Interest rate = 13.32%/12 = 1.11%

n= no of periods = 60 months

Present Value = $13,832.39

So, the Loan amount is $13,832.39

Thus, the amount of car graduate can afford = Loan amount + Down-payment

= $13,832.39 + $16,246.26

= $30,078.65

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