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?

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.

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

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 %.

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)

To find the actual yearly rate of interest in this problem, you would need to calculate the total amount paid over the 15-month period, including the down payment and the monthly payments. Then, you can compare this total with the cash price to find the interest paid.

Let's break down the calculations step by step:

1. Down Payment: $5.00
2. Monthly Payments: $9.00/month for 15 months
Total Monthly Payments: $9.00 x 15 = $135.00
3. Total Amount Paid: Down Payment + Total Monthly Payments
Total Amount Paid: $5.00 + $135.00 = $140.00
4. Cash Price of the Food Processor: $119.50
5. Interest Paid: Total Amount Paid - Cash Price
Interest Paid: $140.00 - $119.50 = $20.50

Now that we know the interest paid is $20.50, we can calculate the annual interest rate. However, we need to convert the 15-month period into a year to find the yearly rate.

To convert the 15-month period into a year, divide it by 12 (the number of months in a year):

15 months ÷ 12 months/year ≈ 1.25 years

Next, divide the interest paid by the total number of years:

Annual Interest Rate = (Interest Paid / Total Amount of Years) x 100
Annual Interest Rate = ($20.50 / 1.25) x 100 ≈ 16.4%

Therefore, the actual yearly rate of interest for this purchase is approximately 16.4%.