Subjects finance

Monthly Payment E6057A

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1. **State the problem:** Jevonte needs to find the monthly payment $M$ for a loan of $P=23000$ with a monthly interest rate $r=0.00325$ (0.325%) over $n=6 \times 12=72$ months. 2. **Formula:** The monthly payment is given by $$M=\frac{P r (1+r)^n}{(1+r)^n - 1}$$ where $P$ is the principal, $r$ is the monthly interest rate, and $n$ is the total number of payments. 3. **Calculate $(1+r)^n$:** $$1+r=1+0.00325=1.00325$$ $$1.00325^{72} \approx 1.2567$$ 4. **Substitute values into the formula:** $$M=\frac{23000 \times 0.00325 \times 1.2567}{1.2567 - 1}$$ 5. **Simplify numerator and denominator:** $$\text{Numerator} = 23000 \times 0.00325 \times 1.2567 = 23000 \times 0.004083775 = 93.926825$$ $$\text{Denominator} = 1.2567 - 1 = 0.2567$$ 6. **Calculate monthly payment:** $$M=\frac{93.926825}{0.2567} \approx 366.1$$ 7. **Round to nearest dollar:** $$M \approx 366$$ **Final answer:** Jevonte's monthly payment is **366** dollars.