Posted by **SSS** on Sunday, August 3, 2014 at 5:40pm.

I'm having a bit of trouble with the following problem. Thanks!

Kevin bought a new car for $22,000. He made a down payment of $5,500 and has monthly payments of $406.69 for 4 years. He is able to pay off his loan at the end of 30 months. Using the actuarial method, find the unearned interest and payoff amount.

- Math -
**Reiny**, Sunday, August 3, 2014 at 6:41pm
balance owing = 22000-5500 = 16500

We don't know the rate, but

if the monthly rate is i , then

16500 = 406.69(1 - (1+i)^-48)/i

Did some alternate numerical calculations and found

n = .007083333..

which makes it an annual rate of 8.5% compounded monthly

So balance owing after 30 months

= 16500(1.00708333..)^30 - 406.69(1 - 1.00708333^-30)/.007083333..

= $9434.63

Can you take it from there ?

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