Question

You wish to buy a car in 2.5 years and would like to start saving now for the down payment. Figure a 15 % down payment. Target price will be $65000. You currently have the ability to earn an after tax rate of 9.5% on investments. When you purchase the car you plan to finance it at 2.9% for 4 years.

How much will you be financing when the time comes? How do you find that amount?

What calculation will be required to figure out the amount invested? How much will you invest?

How much will you owe for the monthly car payment? What will be the total interest you will pay on the loan?

If you chose to finance the total amount, how much more would you need for each payment? How much more interest would you pay over the life of the loan

Answer 1

Solution :-

Target Price of Car = $65,000

Down Payment = 15% * $65,000 = $9,750

(A) Amount Financed = $65,000 - $9,750 = $55,250

(B) For the Down Payment Amount we needs to find present value of down payment

= $9,750 / ( 1 + 0.095 )² ( 1 + 0.0475 ) = $7,762.87

(C) Rate of Finance = 2.9%

Interest for a month = 2.9 / 12 = 0.241667%

total payments = 4 * 12 = 48

Monthly Car Payment = Amount Financed / PVAF ( 0.24167% , 48 )

= $55,250 / PVAF ( 0.24167% , 48 )

= $55,250 / 45.269

= $1,220.48

Interest paid on the loan = ( 48 * 1,220.48 ) - $55,250

= $33,33.10

(D) If finance full target Price that is $65,000

Value of installment =

Monthly Car Payment = Amount Financed / PVAF ( 0.24167% , 48 )

= $65,000 / PVAF ( 0.24167% , 48 )

= $65,000 / 45.269

= $1,435.86

Interest paid on the loan = ( 48 * 1,435.86 ) - $65,000 = $3,921.29

Excess interest paid = $3,921.29 - $33,33.10 = $588.19

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