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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.

  • Math -

    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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