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March 30, 2017

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Henry bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest did Henry pay?

1 - 14.55
2 - 29.09
3 - 34.38
4 - 68.75

  • Math - ,

    Here is a quick approximate way to do it. Otherwise you need a much more complicated method, or some website that uses Java to do it for you.

    (320 - 20)/2 = $150 was the average balance during payoff.
    Total interest payments were (340-320) = $20
    (5/6 yr)* %150*I (per yr) = $20
    I = 0.16 = 16%
    It is actually a bit lower than that, because the average balance is a bit higher than $150. So I'd got with 14.55%

  • Math - ,

    Henry bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest did Henry pay?

    1 - 14.55
    2 - 29.09
    3 - 34.38
    4 - 68.75

    The monthly payment to pay off a loan derives from R = Pi/[1 - (1+i)^-n] where R = the monthly payment (or rent), P = the loan amount (or principal, n = the number of interest bearing periods and i = the yearly interest rate divided by 100(12).

    R = 34
    P = 300
    i = I/100(12)annualized
    n = 10 months
    Therefore, 34 = 300i/[1 - (1+i)^-10].
    By trial and error, I reached a yearly interest rate of 29.09%, or close enough for our purposes, 29% gives me a monthly payment of $34.13.

    For 29%, i = .29/12 = .024166666...
    R = 300(.024166666)/[1 - 1.024166666)^-10] = $34.13 per month.

    You can play around with the % to get exactly $34 if you wish.

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