Bus. Math

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

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  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

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