Monthly amortization schedule. Sherry and Sam want to purchase a condo at the coast. They will spend \( \$ 650,000 \) on the condo and are taking out a loan for the condo for twenty years at \( 7.3 \% \) interest. a. What is the monthly payment on the mortgage? Construct the amortization of the loan for the twenty years in a spreadsheet to show the interest cost, the principal reduction, and the ending balance each month. b. Then change the amortization to reflect that after ten years, Sherry and Sam will increase their monthly payment to \( \$ 7,600 \) per month. When will they fully repay the mortgage with this increased payment if they apply all the extra dollars above the original payment to the principal? a. What is the monthly payment on the mortgage? The monthly interest rate on the mortgage is \( \square \% \). (Round to seven decimal places.)

To find the monthly payment on the mortgage, first, we'll use the formula for monthly payment calculation: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where: - \( M \) is the total monthly mortgage payment. - \( P \) is the principal loan amount (\$650,000). - \( r \) is the monthly interest rate (annual rate \( 7.3\% \) divided by 12). - \( n \) is the number of payments (loan term in months). The monthly interest rate is calculated as: \[ r = \frac{7.3\%}{12} = 0.0060833 \quad (\text{rounded to seven decimal places}) \] The number of payments for a 20-year mortgage is: \[ n = 20 \times 12 = 240 \text{ months} \] Substituting the values into the payment formula, we get: \[ M = 650,000 \times \frac{0.0060833(1 + 0.0060833)^{240}}{(1 + 0.0060833)^{240} - 1} \] Solving this, the monthly payment \( M \) comes out approximately to be \$4,683.32. Next, let's discuss the notion of amortization schedules! You can visualize this over twenty years by creating a detailed spreadsheet that would track your payments, showing how much goes toward interest versus principal each month. Just think of it as a financial diary where each entry reveals how much closer you are to owning your condo outright! Now, if Sherry and Sam increase their payment to \$7,600 after ten years, this will significantly reduce the principal balance. A fun way to approach this is by calculating how many fewer months it will take to pay off the remaining mortgage after this change - it’s like a financial race against the clock! Keep in mind, applying everything over the original monthly payment towards the principal accelerates the loan payoff, and they could see their dream condo fully paid off much sooner than they think!