# 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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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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