math

Tim Worker buys a new sofa for $629.95. He pays 25% down and takes an installment loan to complete the purchase. He makes 12 payments which include his principal and a $60.00 finance charge. What is the APR on his loan to the nearest tenth? The down payment is? The amount financed is? The monthly payment will be? At the end of one year the monthly payments will total? The finance charge for one year ÷ amount financed is?

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  1. downpayment = 629.95(.25) = $157.49

    amount to be financed = 472.46

    The rest of the question sounds like something from the last century.
    A very silly way of doing the financing and it misleads the uninformed.

    I will assume they will now take 472.46 , add on $60 to get $532.46
    then divide that by 12 to get a monthly payment of
    $532.46/12 or $44.37

    so to find the rate of interest actually charged:
    472.46 = 44.37 (1 - (1+i)^-12)/i
    10.64773576 i = (1 - (1+i)^-20)

    an extremely difficult equation to solve
    I will use Wolfram to attempt it.
    (had to change the i to x, or else it interpreted i as
    √-1 )
    I used : 10.6477= (1 - (1+x)^-20)/x
    http://www.wolframalpha.com/input/?i=solve+10.6477%3D+%281+-+%281%2Bx%29%5E-20%29%2Fx

    and got .06935 as you can see
    so the monthly rate is .06935 and the annual rate is .06935(12) = .8322

    or 83.22%
    ( and they burned people at the stake in the middle ages for such practises)

    check on my rate
    if annual rate is 83.22% , then monthly rate = 6.935% or .06935

    let the monthly payment be p
    then 472.46 = p( 1 - 1.06935)^-20)/.06935
    472.46 = p(10.6477..)
    p = 44.37 , (not bad)

    I suppose the intent is for the unscrupulous dealer to suggest that the interest is only $60 on $472.46 for 1 year
    or 60/472.46 = .12699
    or 12.7% interest and telling them it is a lot better than the 18%+ rate that a credit card will charge.

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