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
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
To calculate the unpaid balance at the end of a specific time period, you can use the formula for the present value of an ordinary annuity.
The formula is:
PV = PMT * [1 - (1 + i)^-n] / i
Where:
PV is the present value or unpaid balance
PMT is the monthly payment
i is the interest rate per period (in this case, per month)
n is the number of periods
For the first calculation, let's determine the unpaid balance at the end of 12 months.
Using the formula, we have:
PV = 804.45 * [1 - (1 + 0.0075)^-12] / 0.0075
PV ≈ $9,198.82
So, you are correct with your calculation for the unpaid balance at the end of 12 months.
For the second calculation, finding the unpaid balance at the end of 72 months, you can use the same formula:
PV = 804.45 * [1 - (1 + 0.0075)^-72] / 0.0075
PV ≈ $44,628.35
Again, you are correct with your calculation for the unpaid balance at the end of 72 months.
You can input this calculation into a calculator using the appropriate operations and parentheses. Make sure to use the correct interest rate per period (in this case, 0.0075 for 9% per year compounded monthly) and the number of periods (12 for 12 months and 72 for 72 months).