To solve this problem using a financial calculator, we need to identify the variables based on the information provided:
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N (Total number of periods): This is the total number of payments in the mortgage. Since Derek has a 30-year mortgage and makes monthly payments, this would be: \[ N = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ months} \]
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i/y (Interest rate per period): The annual interest rate is given as 4.36%. Since payments are monthly, we need to convert this to a monthly interest rate: \[ i/y = 4.36% / 12 = 0.3633% \text{ per month} \quad \text{(as a decimal, this is } 0.0436 / 12 \approx 0.003633\text{)} \]
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PV (Present Value): This is the amount borrowed, which is the loan amount: \[ PV = 332,415.00 \]
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PMT (Payment): Since we are interested only in how much Derek owes after making 108 payments, we'll need to calculate the monthly payment first using the N, i/y, and PV. The formula for calculating the monthly payment is: \[ PMT = PV \times \frac{i/y}{1 - (1 + i/y)^{-N}} \] Plugging the numbers in: \[ PMT = 332,415 \times \frac{0.003633}{1 - (1 + 0.003633)^{-360}} \]
You can compute this value using a financial calculator or Excel.
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FV (Future Value): After making 108 payments, we need to find out how much Derek still owes, which is the remaining balance of the mortgage. Therefore, it would be calculated using the remaining periods (N = 360 - 108 = 252) and PMT that we just calculated. The FV we are trying to find will be the remaining balance after 108 payments.
A summary of what you'd input on the financial calculator:
- N = 360
- i/y = 0.3633% or 0.003633 as a decimal
- PV = -332,415 (usually entered as a negative because it's an outflow)
- PMT = calculated value from above
- FV = 0 (you’re calculating how much is owed, so you will use 0 here)
After calculating the PMT, you can then set the financial calculator for the remaining periods (N = 252), input the other values (PV = -332415, PMT as calculated, and FV = 0) to calculate how much Derek owes after 108 payments.
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