Question 979459: A $5,000 debt on a credit card will take 32 years to repay if only the minimum monthly payment is made. This debt will cost the borrower about $7,800 in interest. The borrower could be out of debt in 3 years by paying $175 per month. Find the amount of interest paid at the end of 3 years.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A debt of $5,000 paid over 32 years with a total interest paid of only $7,800 must involve larger payments at the beginning and smaller payments later, based on the balance at the time of the payment.
Calculations could be complicated.
However, that seems not to matter to solve the problem.
If a $5,000 debt he total can be paid in 3 years by paying $175 per month,
the total amount paid over those 3 years is
 .
That amounts to repaying the  original debt plus interest amounting to
 , and that is what I believe the problem is asking for.
NOTES:
That $175 monthly payment means
an interest rate of 15.68% per year,
compounded monthly,
with payments made at the end of each month.
The interest paid on the first month would be $65.33.
The difference, $175 - $65.33 = $109.67, would be applied to reduce the balance owed.
If only $65.33 was paid at the end of each month,
the loan balance would be $5,000 after each monthly payment,
and it would take eternity to repay the loan.
With a payment only a little larger than $65.33 (let's say $66, or $70) at the end of each month,
the loan would be fully paid in less than 32 years,
but then, the total amount paid,
and the total interest paid would be a lot more.
To pay only $7,800 in interest, and still take 32 years to repay,
larger payments are needed at the beginning,
when the balance and the monthly interest owed is larger.
Credit cards' minimum payments are based on balance,
such as 1/50 of the balance or a fixed quantity (whichever is less),
so minimum payments are larger at the beginning.
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