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Question 1089194: I bought a car for $4200 and put $500 deposit in that left $3700 to pay and I paid $44 a week for 104 weeks the interest I paid was $980 at what rate of interest was I charge. and could you show me how to work out the answer
thank you . Aileen price .plnajprice@gmail.com
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the calculation of the interest rate depends on the type of loan.
some loans charge you interest rate on the remaining balance.
other loans charge you interest rate on the original balance.
what you pay each week will be the same, but the interest rate will be different.
for example, assuming equal payments of 44 dollars a week, then:
on a remaining balance type loan, the interest rate will be approximately 21.8% on the remaining balance.
the total interest paid would be 104 * 44 - 3700 = 876 dollars which is a little less than 980.
the weekly payment would have to be 45 dollars a week for the total interest paid to be equal to 980 dollars.
104 * 45 - 3700 = 980.
when the payments are 45 dollars a week, the annual interest rate is approximately 24.3% per year on the remaining balance.
if you are doing a simple interest rate calculation, then the interest rate is different, even though the payments are the same.
since payment of 45 dollars a week seemed to work better for the compound interest type calculation, i'll assume 45 dollars a week for the simple interest type calculation also.
if you paid 45 dollars a week for 104 weeks then you paid a total of 45 * 104 = 4780 dollars.
since the original loan is 3700, then you paid a total of 980 interest.
with a simple interest calculation, the formula if i = p * r * n where i is the interest and p is the principal and r is the interest rate per time period and n is the number of time periods.
the formula becomes 980 = 3700 * r * 104
solve for r to get r = 980 / 3700 / 104 = .0025467775 * 100 = .25467775 * 52 = approximately 13.25% simple interest rate per year.
your total payments are the same and your total interest is the same but the interest rate is different.
in other words, you would be comparing apples and oragnes and they don't compare very well.
the 24% is on the remaining balance.
the 13% is on the original balance.
i took the time to give you detailed calculations so you can see what i mean.
those calculations are done in excel.
i took a picture of the first 5 weeks and the last 5 weeks so you can see what i mean.
the first picture shows remaining balance at about 24% per year interest rate.
the second picture shows simple interest at about 13% per year interest rate.
the point here is that the sum total of your payments is the same, but the interest rate is different.
in the first picture, the interest rate of 24% per year compounded weekly is applied to the remaining balance of each week.
in the second picture, the interest rate of 13% per year translated to weekly is applied to the original balance regardless of the week.
you have paid the same total amount of money for the same number of weeks.
the interest rate, however, is not the same because the first picture it is applied to the remaining balance and the second picture it is applied to the original balance.
same payments, different interest rate.
bottom line:
in order to determine the interest rate, you need to know the type of loan and how the interest rate was calculated.
if they're telling you 13%, then it was probably a fixed interest type loan.
if they're telling you 24%, then it was probably a remaining balance type loan.
either way, you paid the same amount of money for the same amount of weeks.
the reality might even be something different since there are not the only 2 types of loans available.
i believe there are other.
you need to go back to the lender and find out how he determined that the interest you paid was 980.
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