For C1 use the PV-of-annuity formula to conjure up the required monthly payment:
^n}}{r/12} )
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.
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