The Taylors have purchased a $290,000 house. They made an initial down payment o

Question

The Taylors have purchased a $290,000 house. They made an initial down payment o $40,000 and secured a mortgage with interest charged at the rate of 8% /year on the unpaid balance. Interest comput your answer to the nearest cent.) ations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Rou is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent) 5 years 10 years $ 20 years Need Help? Road t

Explanation / Answer

Answer 1 We can use the present value of annuity formula to calculate the monthly loan payment. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan amount = $290000 - $40000 = $250000 P = Periodic payment i.e. Monthly loan payment = ? rate of interest per month = 8%/12 = 0.006667 n = no.of months = 30 years * 12 = 360 250000 = P*{[1-(1+0.006667)^-360]/0.006667} 250000 = P*136.28 P = 1834.41 Monthly loan payment = $1834.41 Answer 2 Calculation of Loan balance after 5 years and Equity We can use the present value of annuity formula to calculate the loan balance after 5 years. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan balance = ? P = Monthly loan payment = $1834.41 rate of interest per month = 8%/12 = 0.006667 n = no.of months remaining = 25 years * 12 = 300 PV of annuity = 1834.41*{[1-(1+0.006667)^-300]/0.006667} PV of annuity = 1834.41*129.56 = 237674.64 Loan balance after 5 years = $2,37,674.64 Equity after 5 years = Cost of home - Loan balance after 5 years = $290000 - $237674.64 = $52,325.36 Answer 3 Calculation of Loan balance after 10 years and Equity We can use the present value of annuity formula to calculate the loan balance after 10 years. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan balance = ? P = Monthly loan payment = $1834.41 rate of interest per month = 8%/12 = 0.006667 n = no.of months remaining = 20 years * 12 = 240 PV of annuity = 1834.41*{[1-(1+0.006667)^-240]/0.006667} PV of annuity = 1834.41*119.55 = 219311.76 Loan balance after 10 years = $2,19.311.76 Equity after 10 years = Cost of home - Loan balance after 10 years = $290000 - $219311.76 = $70688.24 Answer 4 Calculation of Loan balance after 20 years and Equity We can use the present value of annuity formula to calculate the loan balance after 20 years. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan balance = ? P = Monthly loan payment = $1834.41 rate of interest per month = 8%/12 = 0.006667 n = no.of months remaining = 10 years * 12 = 120 PV of annuity = 1834.41*{[1-(1+0.006667)^-120]/0.006667} PV of annuity = 1834.41*82.42 = 151194.91 Loan balance after 20 years = $1,51,194.91 Equity after 20 years = Cost of home - Loan balance after 20 years = $290000 - $151194.91 = $1,38,805.09

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