SOLUTION: Your credit card has a balance of ​$3100 and an annual interest rate of 12​%. You decide to pay off the balance over five years. If there are no further purchases charged to th

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Question 1205155: Your credit card has a balance of ​$3100 and an annual interest rate of 12​%. You decide to pay off the balance over five years. If there are no further purchases charged to the​ card, you must pay ​$68.96 each​ month, and you will pay a total interest of ​$1037.60. Assume you decide to pay off the balance over one year rather than five. How much more must you pay each month and how much less will you pay in total​ interest?
Use PMT=
P
r
n
1−1+
r
n−nt to determine the regular payment amount.
Question content area bottom
Part 1
You will pay ​$ more each month.
​(Round to the nearest cent as​ needed.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The formula you provided is very garbled.
But if I had to guess, the formula your teacher wants you to use is
PMT+=+%28P%2A%28r%2Fn%29%29%2F%281+-+%281%2Br%2Fn%29%5E%28-n%2At%29%29
where,
  • P = principal = starting balance
  • r = annual interest rate in decimal form
  • n = compounding frequency
  • t = number of years
If we plug in this set of values
  • P = 3100
  • r = 0.12
  • n = 12
  • t = 5
then we get,
PMT+=+%28P%2A%28r%2Fn%29%29%2F%281+-+%281%2Br%2Fn%29%5E%28-n%2At%29%29

PMT+=+%283100%2A%280.12%2F12%29%29%2F%281+-+%281%2B0.12%2F12%29%5E%28-12%2A5%29%29

PMT+=+68.957788

PMT+=+68.96
which matches with what the instructions mentioned.

Now let's change t = 5 to t = 1.
Everything else stays the same.
PMT+=+%28P%2A%28r%2Fn%29%29%2F%281+-+%281%2Br%2Fn%29%5E%28-n%2At%29%29

PMT+=+%283100%2A%280.12%2F12%29%29%2F%281+-+%281%2B0.12%2F12%29%5E%28-12%2A1%29%29

PMT+=+275.431245

PMT+=+275.43
use this financial calculator to verify
https://www.calculatorsoup.com/calculators/financial/loan-calculator.php
or
https://www.bankrate.com/loans/loan-calculator/
There are many other calculators found online.
The PMT function can be used in a spreadsheet.

Subtract the payment amounts to find how much more you pay per month.
275.43 - 68.96 = 206.47
You'll pay $206.47 more per month if you go with the 1 year option rather than 5 year option.

Multiply the monthly payment with the number of months to figure out how much money is paid back.
  • Five year option: ($68.96 per month)*(60 months) = $4137.60
  • One year option: ($275.43 per month)*(12 months) = $3305.16
Then subtract 3100 from each result to find the total interest paid back.
  • Five year option: $4137.60 - $3100 = $1037.60 (matches what the instructions mentioned).
  • One year option: $3305.16 - $3100 = $205.16
Subtract those results to find the savings
$1037.60 - $205.16 = $832.44
Or we could have subtracted the amounts paid back
$4137.60 - $3305.16 = $832.44
This works because the principal amounts will cancel.
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Summary:

You will pay $206.47 more each month.
But you save $832.44 in total interest.