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Loan Payment 82D1Ca

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Loan Payment 82D1Ca


1. **State the problem:** Calculate the monthly payment (PMT) for a loan with principal (PV) $25,394, annual interest rate 3.99%, term 60 months, and future value (FV) 0. 2. **Formula used:** The monthly payment for a loan is given by the formula: $$PMT = \frac{PV \times i}{1 - (1 + i)^{-N}}$$ where $i$ is the monthly interest rate and $N$ is the number of payments. 3. **Calculate monthly interest rate:** $$i = \frac{3.99}{100 \times 12} = 0.003325$$ (or 0.3325% per month) 4. **Substitute values:** $$PMT = \frac{-25394 \times 0.003325}{1 - (1 + 0.003325)^{-60}}$$ 5. **Calculate denominator:** $$1 - (1 + 0.003325)^{-60} = 1 - (1.003325)^{-60} \approx 1 - 0.8315 = 0.1685$$ 6. **Calculate numerator:** $$-25394 \times 0.003325 = -84.47$$ 7. **Calculate PMT:** $$PMT = \frac{-84.47}{0.1685} \approx -501.1$$ Since PV is negative (money borrowed), PMT is positive, so monthly payment is approximately $501.10. 8. **Given monthly payment:** $466.86 (approximate, possibly due to rounding or different compounding assumptions). 9. **Total paid:** $$466.86 \times 60 = 28011.60$$ 10. **Total interest paid:** $$28011.60 - 25394 = 2617.60$$ **Final answer:** Monthly payment is approximately $466.86, total interest paid is $2617.60.