Question 1118666: Larry borrows $12000 to be repaid at 12% p.a. at rate of interest over 4 years.
a. Calculate the interest that Larry must pay.
b. What is the total amount that Larry must repay?
c. If Larry repays the loan in equal annual instalments, calculate the amount of each repayment.
But could you just answer question c please.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you did not specify the type of loan.
is it flat rate or is it compound rate from the remaining balance?
if flat rate, the formula would be:
i = p * r * n
i is the interest
p is the principal
r is the interest rate per time period
n is the number of time periods
in your problem, the formula becomes:
i = 12000 * .12 * 4
this results in i = 5760.
that would be the total interest that would be paid after 4 years.
the total amount that would have to be repaid is the principal plus the interest.
that would be 12000 + 5760 = 17760.
he would more then likely pay this in equal installments of 17760 / 4 = 4440 per year.
if the loan type is compound interest on the remaining balance, then a different calculation is required.
while there are formulas to allow you to calculate this manually, it is best solved by using a financial calculator.
one such calculator can be found at https://arachnoid.com/finance/
you would need to find the annual payments required before determining what the total interest is to be repaid.
here are what the inputs look like for that calculation.
here is what the output looks like.
the total interest paid would be 4 * 3950.81 minus 12000 = 3803.52.
that's the payment amount times the number of payments minus the initial loan amount.
in the flat rate loan, the interest is calculated off the original amount of the loan.
in the remaining balance loan, the interest is calculated from the remaining balance at the end of each time period.
for the same interest rate, you will pay less overall interest with the remaining balance type loan.
not knowing what type of loan you are talking about, i calculated for what type i know they usually are.
to summarize.
with flat rate type loan:
a. Calculate the interest that Larry must pay.
interest = 5760.
b. What is the total amount that Larry must repay?
total amount to be be repaid is 17760.
c. If Larry repays the loan in equal annual installments, calculate the amount of each repayment.
amount of each payment would be 4440.
with compound interest remaining balance type loan:
a. Calculate the interest that Larry must pay.
interest = 3803.25.
b. What is the total amount that Larry must repay?
total amount to be repaid is 15803.25.
c. If Larry repays the loan in equal annual instalments, calculate the amount of each repayment.
amount of each payment would be 3950.81.
note that in the compound interest remaining balance type loan, you need to calculate the payment required before you can calculate the total interest to be paid.
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