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

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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) About Me  (Show Source):
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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(10551) About Me  (Show Source):
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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: highlight_green%28matrix%281%2C3%2C+203.86%2860%29%2C+%22=%22%2C+%22%2412%2C231.44%22%29%29
IGNORE all other RIDICULOUS, NON-SIMILAR answers.

Answer by greenestamps(13198) About Me  (Show Source):
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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

A+=+P%28%281-%281%2Br%2Fn%29%5E%28-%28n%2At%29%29%29%2F%28r%2Fn%29%29

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(52776) About Me  (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

        P =  A%2A%28%28r%2Fn%29%2F%281+-+%281%2Br%2Fn%29%5E%28-n%2At%29%29%29.

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

        P  =  9000%2A%28%280.128%2F12%29%2F%281+-+%281%2B0.128%2F12%29%5E%28-12%2A5%29%29%29 = $203.86.

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