Question 1120632: off with monthly payments where f is the finance charge on the Loan p is the number of payments and b is the original amount of the loan find the approximate annual interest rate for an automobile loan to be repaid in 36 monthly installments if the finance charge on the loan is $284.00 and the original loan balance is $3380 (round answer to two decimal places).
a.5.45%
b. 5.76%
c. 5.14%
d.5.6 %
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = finance charge on the loan.
p is the number of payments.
b is the original amount of the loan.
loan is to be repaid in 36 monthly installments.
finance charge on the loan is 284.
original loan balance is 3380.
total amount to be repaid in 36 months is 3380 + 284 = 3664.
divide that by 36 months to get a payment of 101.777777777... per month.
i get:
present value = 3380
monthly payment = 101.777777777...
number of payments = 36
i put these into the following online calculator and i get a monthly interest rate of 0.442776%
multiply that by 12 and i get a yearly interest rate of 5.313312%.
that doesn't match any of your answers.
my assumption is that payment is made at the end of each period which is standard.
if i make payment at the beginning of each period, i get a monthly interest rate of 0.468997%.
multiply that by 12 and i get a yearly interest rate of 5.627964%.
that's close to 5.6% but not exactly.
the basic procedure is:
the total amount to be repaid is the principal plus the finance charge.
this is equal to 3380 + 284 = 3664.
divide that by the number of payments to get 3664 / 36 = 101.77777777... payment per month.
inputs to the calculator are therefore:
present value = amount of loan = 3380.
number of payments is 36.
amount of each payment is -101.7777777777.....
payment are normally made at the end of each month, so set that to end of month payments.
future value = 0 since your balance should be 0 at the end of the 36 month period.
i don't know what was done to give you the selections that you got, nor what assumptions were made.
the best i can do is assume the normal loan processing methods which i did.
if you have a formula that you should be following, then use that formula.
my manual formulas would yield the same results that the calculator gave me.
i tried rounding the payment to 1.78 per month but that didn't make much of a difference and i got annual interest rate of 5.31% with end of month payments.
so, no cigars and, unless i know what formula or assumptions are going into this problem, i don't have an answer that you can use.
my results are:
with end of month payments, i get 5.31% per year.
with beginning of month payments, i get 5.62% per year.
my results are shown below:
with end of month payments, interest rate = .442897 [ercemt per month * 12 = 5.314764 percent per year.
with beginning of month payments, interest rate = .468997 percent per month * 12 = 5.627964 percent per year.
without any additional information about how these payments are supposed to be calculated, i can't help you any further.
here are the results of my use of the calculators.
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