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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.

User Icon for Reiny Reiny answered
10 years ago

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 ?