math

A food processer for $119.50 cash, $5.00 down and $9.00 a month fer 15 months. how would i find the actual yearly rate of interest of this problem?

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asked by julie
  1. The amount financed was $119.50 - 5.00 down = $114.50.
    How much was paid in monthly payments?
    That was $9.00/mo x $15 mo = $135.00
    How much interest was paid? That's $135.00-$114.50 = $20.50

    $20.50 is what part of 114.50?
    20.50/114.50 = 0.l790 over a period of 15 months; therefore, per month this was 0.1790/15 = 0.01194/month and that times 12 months to a year = 0.1432. Changing that to percent = 14.32%/year. Check my thinking. Check my work.

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  2. the answer says 26.86% but i understand what you did.

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    posted by julie
  3. The answer of 26.86 was obtained by using a rather archaic estimation formula which says:
    rate = 24I/((balance(number of payments+1))

    so rate = 24*20.5/(114.5*16)
    = .26855 or 26.86%

    I set it up with the compound interest formula

    Present Value = Paym( 1 - (1+i)^-n)/i

    114.5 = 9(1 - (1+i)^-15)/i

    I used interpolation and a rather "fancy" technique to solve that equation and to get
    i = .02133 per month or .25599 per year
    or 25.599 %.

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    posted by Reiny
  4. I knew I was out of my league when I worked that problem but the answer sounded reasonable to me so I posted it. Now you know why store clerks like to see me coming. :0)

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