Question

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

Answer 1

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