1. **State the problem:** We are given the equation $$155,000 = m \frac{1 - (1 + \frac{0.041}{12})^{-12 \times 15}}{\frac{0.041}{12}}$$ and need to solve for the monthly payment $m$. 2. **Identify the formula:** This is the formula for the present value of an annuity, commonly used in loan amortization: $$P = m \times \frac{1 - (1 + r)^{-n}}{r}$$ where $P$ is the loan amount, $m$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. 3. **Plug in the known values:** - $P = 155000$ - $r = \frac{0.041}{12} = 0.0034166667$ - $n = 12 \times 15 = 180$ 4. **Rewrite the equation to solve for $m$:** $$m = P \times \frac{r}{1 - (1 + r)^{-n}}$$ 5. **Calculate the denominator:** $$1 + r = 1 + 0.0034166667 = 1.0034166667$$ $$-n = -180$$ $$ (1 + r)^{-n} = 1.0034166667^{-180} = \frac{1}{1.0034166667^{180}}$$ Calculate $1.0034166667^{180}$: $$1.0034166667^{180} = e^{180 \times \ln(1.0034166667)}$$ Approximate $\ln(1.0034166667) \approx 0.003410$ $$e^{180 \times 0.003410} = e^{0.6138} \approx 1.847$$ So, $$(1 + r)^{-n} = \frac{1}{1.847} = 0.541$$ 6. **Calculate the denominator:** $$1 - 0.541 = 0.459$$ 7. **Calculate $m$:** $$m = 155000 \times \frac{0.0034166667}{0.459}$$ Simplify the fraction: $$\frac{0.0034166667}{0.459} \approx 0.00744$$ 8. **Final monthly payment:** $$m = 155000 \times 0.00744 = 1153.2$$ **Answer:** The monthly payment $m$ is approximately **1153.20**.