Thread: Annuity

phrong wants to purchase a motorcycle. he can borrow $6500 at 10%/a, compounded quarterly, if he agrees to repay the loan by making equal quarterly payments for 4 years. what is a resonable quarterly payment. this is asking for a estimate. can u explain how i would go about making a estimate?

One decent way to find an estimate would be to find the average between the initial amount borrowed and the value of the borrowed money at the end of four years, then find how much, paid each icp, would cover that amount if the interest rate were zero.

For instance, if 5000 was the loan amount, and i = 10%/annum, compounded quarterly, then the loan would be valued at 5000*(1.025)^16, or nearly 7423, at the end of the four years. The average value would be (5000+7423)/2 = 6211.5, and so, the quarterly payment covering that amount if i = 0% is 6211.5/16, which is around 388.

Using an annuity immediate with PMT = 388, the PV of the payments is 5065, which is fairly close to 5000. Thus, the estimate is decent, without having to calculate the annuity.

Anyway, that's just a thought. It's been a few years since my math of finance class.