SOLUTION: Hannah has taken out a personal loan for $9000, which she will pay off with 60 monthly payments starting 1 month from now. The interest rate is 12.8% compounded monthly. Determine

Question 1133119: Hannah has taken out a personal loan for $9000, which she will pay off with 60 monthly payments starting 1 month from now. The interest rate is 12.8% compounded monthly. Determine the total amount Hannah will pay over the 60 months?
Found 4 solutions by rothauserc, MathTherapy, greenestamps, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
The compound interest formula is
:
A = P * (1 +(r/n))^(nt), where P is the principal amount, r is the rate, n is the number of times the interest is compounded per year, t is the time in years and A is the future value of the loan including interest.
:
For this problem, P is $9000, r is 0.128, n is 12 and t is 5 years(60/12)
:
A = 9000 * (1 +(0.128/12))^(12*5) = 17010.5769 is approximately 17010.58
:
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The total amount Hannah will pay over the 60 months is $17,010.58
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:

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hannah has taken out a personal loan for $9000, which she will pay off with 60 monthly payments starting 1 month from now. The interest rate is 12.8% compounded monthly. Determine the total amount Hannah will pay over the 60 months?

Monthly payment on a $9,000 loan for 5 years @ COMPOUND interest rate of 12.8%: $203.86.
Amount paid in 5 years, or in 60 months:
IGNORE all other RIDICULOUS, NON-SIMILAR answers.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

This is not a problem about compound interest; it is a problem about repaying a loan.

The formula for determining the amount of each payment, A, with a loan amount of P, an annual percentage rate of r, with payments n times per year, for t years, is

In this problem, P = 9000; r = 12.8% = 0.128; n = 12; and t = 5. The amount of each payment is then what the other tutor shows, $203.86.

Then the total amount Hannah will pay over the 60 months is 60 times that payment amount.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            In the post by @greenestamps, the formula for the monthly payment to repay the loan is presented incorrectly

                (although the final answer is correct !)

            I came to provide a correct formula.

See this Wikipedia article Mortgage_calculator https://en.wikipedia.org/wiki/Mortgage_calculator

Solution

The formula for determining the amount of each payment, P, with a loan amount of A, an annual percentage rate of r,
with payments n times per year, for t years, is

         = .

In this problem, A = 9000; r = 12.8% = 0.128; n = 12; and t = 5. The amount of each payment is then

         = = $203.86.

The total amount Hannah will pay over the 60 months is 60 times that payment amount.

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