David takes out a conventional loan to purchase a car loan. The interest rate is 4.8% compunded quarterly and david has four years to repay the 8000 dollars he borrowed. What are davids quarterly payments.
Please show how you reached your conclusion.
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Phineas Bogg
May 28th, 2010 04:14 AM
Let p be the value of David’s quarterly payments. The present value of David’s first payment is:
p/(1 + .048/4), since the interest rate is 4.8% and 1/4 of a year has gone by.
Similarly the present value of his nth payment is:
p/(1+.048/4)^n
So the total present value of the 16 payments is:
p*[1.012^-1 + ... + 1.012^-16]
Using a formula for a finite geometric sum
= p(1 – 1.012^-16)/.012
Now setting this equal to 8000 we get:
p = 8000*.012/(1-1.012^-16)
Punch these numbers into your calculator to get:
p = $552.52
I like to do a little sanity check on these kind of problems just to make sure my answer is in the ballpark. If the interest rate were 0, the quarterly payment would be just 8000/16 = 500. Since have an interest rate greater than 0 would raise the payment, $552.52 seems about right.