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To calculate how quickly you would need to pay off the truck at 8.7% interest to simulate a 3% interest rate over 6 years, you can use the concept of present value and equate the total amount paid at 8.7% interest to the amount you would pay at 3% interest.
Here's the step-by-step calculation:
1. Calculate the monthly payment required at 3% interest over 6 years using the present value formula:
PV = Payment × [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value (amount borrowed, $22,000 in this case)
Payment = Monthly Payment
r = Monthly Interest Rate
n = Total number of payments (6 years * 12 months/year = 72 months)
At 3% interest:
r = 3% / 100 / 12 = 0.0025 (monthly interest rate)
PV = $22,000
Rearranging the formula to solve for Payment:
Payment = PV / [(1 - (1 + r)^-n) / r]
Payment = $22,000 / [(1 - (1 + 0.0025)^-72) / 0.0025]
Payment ≈ $328.38
2. Calculate the total amount paid at 3% over 6 years by multiplying the monthly payment by the total number of months:
Total amount paid at 3% = Payment × Total number of payments
Total amount paid at 3% = $328.38 * 72
Total amount paid at 3% ≈ $23,638.56
3. Now, calculate the total amount you would pay at 8.7% interest over the same 6-year period:
Use the formula for the total amount paid on a loan:
Total amount paid at 8.7% = Loan Amount + Total Interest
Loan Amount = $22,000
Total Interest at 8.7% = Total amount paid at 8.7% - Loan Amount at 8.7%
Total Interest at 8.7% = $23,638.56 - $22,000
Total Interest at 8.7% ≈ $1,638.56
Total amount paid at 8.7% = $22,000 + $1,638.56
Total amount paid at 8.7% ≈ $23,638.56
The total amount paid at 8.7% interest over 6 years is approximately $23,638.56, which matches the total amount paid at 3% interest over the same period.
Therefore, to simulate a 3% interest rate by paying off the truck at 8.7% interest over 6 years, you'd need to pay approximately $328.38 per month.