[TGHAZNAV0084]

Problem Statement

A friend is considering the purchase of a used car (with a $20,000 price tag) from Truthful Jack Inc. Two financing options are proposed to your friend:

Credit Option: $2,000 down payment and 24 equal monthly payments (with the first payment in one month) at 6% compounded monthly.

Cash Option: Pay $19,500 cash immediately. This option would require your friend to sell her mutual fund units that currently earn 8% compounded quarterly.



C.1 What would be the monthly car payment in the Credit Option?
= 18000 (1+ 0.06/12)^24
= 20288.87/24
= $845.37

C.2 By what percentage (%) would the 10th monthly payment of the Credit Option reduce the outstanding (unpaid) debt?
= 845.37/20288.87 x 100%
=42%
C.3 What cash amount would clear the outstanding debt in the Credit Option immediately after making the 20th monthly payment (your favourite race horse has finally paid handsomely)?
= 845.37 x 20
= 16907.40

therefore 18000-16907.40
= $1092.60

C.4 What would be your friend’s total interest charges (in dollars) if she opted for the Credit Option?
I = 20288.87-18000
= 2288.87
C.5 Which option, Credit or Cash, is better for your friend?
cash is a better option because there is no interest paid on it

[ArcSine]

For C1 use the PV-of-annuity formula to conjure up the required monthly payment:



Where P is the required monthly payment; A is the initial loan amount; r is the annual interest rate (it's being divided by 12 in the formula to arrive at the monthly rate); and n is the number of months (24 in this case).

Easiest way to answer C2 and C3 is to prepare a simple amortization schedule. But note that both of these can be derived algebraically, and you can check your text to see if you've been provided the equations for this purpose.

The C4 answer is just the excess of the total amount paid (24 payments, times the monthly payment amount you'll compute with the formula above) over the initial loan amount. In other words, if you originally borrow 100, and end up paying back 120 (with 5 payments of 24 each, say), then 20 of what you repaid must've been interest.

For C5 you need to determine the present value of the loan option. Discount the cash flows (don't forget the immediate one of 2,000) at 8%, compounded monthly. (Why 8%? Because it's your friend's "opportunity rate"--that is, the rate your friend earns on all funds which remain invested in the mutual fund.) If the loan option has a PV of less than (negative) 19,500 then the loan option is superior. If its PV is greater than (negative) 19,500 then the all-cash option is the way to go.

Note on C5: You can't really say that there's no interest paid on the cash option. OK, true in a technical sense, but economically there's most definitely an interest "cost" associated with the all-cash deal. It's the loss of the interest income that would otherwise be earned on the 19,500 in the mutual fund, were it not pulled out to buy the car. That's why Question C5 has to be decided on the basis of "present value"--it accurately determines which option incurs the lower economic cost in acquiring the car.

[ArcSine]

P.S.: I can see in your answer for C4 that you've certainly got the right idea. You'll just need to re-compute what the total of the 24 payments will be, after you've re-computed the required monthly payment amount. But your thinking on how to arrive at the C4 answer is correct... good job!

[nguyen611]

Hi there,
Ideally if I have the cash I would use it to pay for the car so that interest would not be accrued. This is a great option if you have the cash and also good at saving to build up the cash reserve again. But in this case that you have given I would opt to go with the credit option since cash is not readily available meaning you will have to dip into the mutual fund which she have worked so hard to save. Once withdrawn she may not put all that money she have saved up back into the mutual fund. Other disadvantages to this approach is that you will not earn that quarterly interest that you would otherwise receive, penalties maybe imposed if it is in a fund or retirement account, and taxes would have to be paid for realized gain. By the way if you go with the credit option make sure to change the frequency of your payments to save even more money on our loan. You can read more about this at my site with this link:

MooneyTalk: How to Save Money on your Car Loan without Earning more Income!!

I hope this helps...
-Brian