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Question Hannah signs on a $148,500 mortgage at a 4.5% annual interest rate for 20 years. This results in a monthly payment of $938.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her balance? First let's find the amount of interest she paid in month 1, then find the amount toward reducing the balance.

Question\newlineHannah signs on a $148,500 \$ 148,500 mortgage at a 4.5% 4.5 \% annual interest rate for 2020 years. This results in a monthly payment of $938.48 \$ 938.48 . If only the minimum payment is made in month one, how much of the first payment goes toward reducing her balance?\newlineFirst let's find the amount of interest she paid in month 11, then find the amount toward reducing the balance.

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Q. Question\newlineHannah signs on a $148,500 \$ 148,500 mortgage at a 4.5% 4.5 \% annual interest rate for 2020 years. This results in a monthly payment of $938.48 \$ 938.48 . If only the minimum payment is made in month one, how much of the first payment goes toward reducing her balance?\newlineFirst let's find the amount of interest she paid in month 11, then find the amount toward reducing the balance.
  1. Calculate Monthly Interest: To determine how much of the first payment goes toward reducing the mortgage balance, we first need to calculate the amount of interest charged in the first month. The interest for one month is calculated by taking the annual interest rate, dividing it by 1212 to get the monthly interest rate, and then multiplying it by the current balance of the mortgage.\newlineCalculation: \newlineMonthly interest rate = Annual interest rate / 1212\newlineMonthly interest rate = 4.5%/124.5\% / 12\newlineMonthly interest rate = 0.045/120.045 / 12\newlineMonthly interest rate = 0.003750.00375\newlineInterest for the first month = Mortgage balance ×\times Monthly interest rate\newlineInterest for the first month = $148,500×0.00375\$148,500 \times 0.00375\newlineInterest for the first month = $556.875\$556.875
  2. Calculate Amount Towards Balance: Now that we have the interest for the first month, we can calculate how much of the first payment goes toward reducing the balance. The amount that goes toward the balance is the total monthly payment minus the interest portion.\newlineCalculation:\newlineAmount toward reducing the balance = Total monthly payment - Interest for the first month\newlineAmount toward reducing the balance = $938.48\$938.48 - $556.875\$556.875\newlineAmount toward reducing the balance = $381.605\$381.605

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