To find the monthly payments Derek will have to make on his car loan, we can use the following values for a financial calculator:
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N (Number of periods): Since the loan is for 6 years and payments are made monthly, we calculate the total number of payments: \[ N = 6 \text{ years} \times 12 \text{ months/year} = 72 \text{ months} \]
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PMT (Payment amount): This is what we are trying to find; it will be calculated by the financial calculator.
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i/y (Interest rate per period): Since the interest rate is annual, you need to convert it to a monthly rate by dividing it by 12: \[ i/y = \frac{5.55%}{12} \approx 0.4625% \] In decimal form, this is: \[ i/y = \frac{5.55}{100 \times 12} \approx 0.004625 \]
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PV (Present Value or loan amount): This is the amount Derek borrows: \[ PV = -38655 \quad (\text{negative, because it is an outgoing payment for the borrower}) \] Make sure to input it as a negative value.
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FV (Future Value): For a loan, the future value at the end of the payment period is typically 0, since the loan will be paid off. \[ FV = 0 \]
Summary of Values to Enter:
- N = 72
- PMT = ? (this is what you will calculate)
- i/y = 0.4625 (or input as a percentage if your calculator supports that)
- PV = -38655
- FV = 0
After entering these values into the calculator, compute PMT to find out the monthly payment amount.
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