Frank purchased his house 16 years ago by taking out a 25-year mortgage for $150,000. The mortgage has a fixed interest rate of 5 percent compounded monthly. If he wants to pay off his mortgage today, how much money does he need? He made his most recent mortgage payment earlier today. (Round your intermediate calculation and your answer to two decimal places.)

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To find out how much Frank needs to pay off his mortgage today, we can use the formula for the remaining balance on a mortgage, which is a form of the present value of an annuity formula. The formula to calculate the remaining balance or the payoff amount is:$$P = \frac{rPV}{1 - (1 + r)^{-n}}$$Where:- $P$ is the monthly payment,- $r$ is the monthly interest rate (annual rate divided by 12),- $PV$ is the present value or the initial loan amount,- $n$ is the number of remaining payments.Given:- The initial loan amount ($PV$) = $150,000,- The annual interest rate = 5%, so the monthly interest rate ($r$) = 5% / 12 = 0.0041667,- The total number of payments for a 25-year mortgage = 25 * 12 = 300 payments,- The number of payments made = 16 * 12 = 192 payments,- The number of remaining payments ($n$) = 300 - 192 = 108 payments.First, we need to calculate the monthly payment ($P$), using the formula for the monthly payment on a mortgage, which is:$$P = \frac{rPV}{1 - (1 + r)^{-N}}$$Where $N$ is the total number of payments (300 in this case).$$P = \frac{0.0041667 \times 150,000}{1 - (1 + 0.0041667)^{-300}}$$$$P = \frac{625}{1 - (1 + 0.0041667)^{-300}}$$$$P = \frac{625}{1 - (1.0041667)^{-300}}$$$$P = \frac{625}{1 - 0.2776089}$$$$P = \frac{625}{0.7223911}$$$$P = 865.04$$ (rounded to two decimal places)Now, we use the formula for the remaining balance with the number of remaining payments (108):$$Remaining\ Balance = \frac{0.0041667 \times 865.04}{1 - (1 + 0.0041667)^{-108}}$$$$Remaining\ Balance = \frac{3.60433}{1 - (1.0041667)^{-108}}$$$$Remaining\ Balance = \frac{3.60433}{1 - 0.68886305}$$$$Remaining\ Balance = \frac{3.60433}{0.31113695}$$$$Remaining\ Balance = 11579.39 \times 865.04$$$$Remaining\ Balance = 76,136.95$$Therefore, Frank needs $76,136.95 to pay off his mortgage today.

Frank Purchased His House 16 Years Ago by Taking Out