Posted by Julia H. on Sunday, September 18, 2011 at 10:34pm.
Assuming monthly payment was 804.45 on a 50,000 loan of 9% compound interest for 7 years. How would I calculate what the unpaid balance is and the end of 12 months? Then again a the end of 72 months?
Am I on the right track:
PV .0075 over 1  (1 + i)n
How would I put this in a calculator?
804.45 * { [1  (1.0075)^72] / .0075} = 44,628.35
How would I put this in a calculator?
804.45 * { [1  (1.0075)^12] / .0075} = 9,198.82

Bus. Math  Reiny, Monday, September 19, 2011 at 8:02am
for amount owing after 12 months.
amount of first 12 payments at end of first year
= 804.45( 1.0075^12  1)/.0075 = 10 061.73
Value of debt after 12 months without payments
= 50000(1.0075)^12 = 54 690.34
Balance owing 12 months from now
= 54690.34  10061.73 = 44628.61
Your method makes perfect sense.
You are placing yourself at the 12 month mark on the timeline, with 74 payments still to be made.
So the balance at year 1 must be the PV of the remaining 72 payments.
The second part is also correct.
In my method, I stay at the present (now) on the timeline, showing that there are many ways to do this question.
To do the steps for
804.45 * { [1  (1.0075)^12] / .0075} = 9,198.82 on the calculator, I often start with the difficult parts of the calculation.
here would be my sequence:
1

1.0075^12±
=
÷
.0075
=
x
804.45
=
I got 9198.82 just like you did
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