1. **State the problem:** Juan wants to buy a condo priced at $347,000 with a 20-year amortized loan, putting 10% down to avoid PMI, at an interest rate of 3.4% compounded monthly. We need to find his monthly payment. 2. **Calculate the loan amount:** The down payment is 10% of $347,000, so the loan amount is $347,000 - 0.10 \times 347,000 = 0.90 \times 347,000 = 312,300$. 3. **Identify the formula for monthly payment on an amortized loan:** $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $M$ is the monthly payment, - $P$ is the loan principal, - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of payments (months). 4. **Calculate monthly interest rate and total payments:** - Annual rate = 3.4% = 0.034 - Monthly rate $r = \frac{0.034}{12} = 0.0028333$ - Total payments $n = 20 \times 12 = 240$ 5. **Plug values into the formula:** $$M = 312,300 \times \frac{0.0028333(1+0.0028333)^{240}}{(1+0.0028333)^{240} - 1}$$ 6. **Calculate $(1+r)^n$:** $$ (1+0.0028333)^{240} = (1.0028333)^{240} \approx 1.9996 $$ 7. **Substitute and simplify:** $$M = 312,300 \times \frac{0.0028333 \times 1.9996}{1.9996 - 1} = 312,300 \times \frac{0.005666}{0.9996}$$ 8. **Simplify fraction:** $$\frac{0.005666}{0.9996} \approx 0.005668$$ 9. **Calculate monthly payment:** $$M = 312,300 \times 0.005668 \approx 1,795.21$$ **Final answer:** Juan's monthly payment is $1795.21$. --- **Additional question: Total cost of the condo** 10. Total cost = monthly payment $\times$ number of payments = $1795.21 \times 240 = 430,850.40$ **Final total cost:** $430,850.40$