You plan to purchase a $190,000 house using a 15-year mortgage obtained from you

Question

You plan to purchase a $190,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 4.25 percent. You will make a down payment of 15 percent of the purchase price.

Calculate your monthly payments on this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Calculate the amount of interest and, separately, principal paid in the 25th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Calculate the amount of interest and, separately, principal paid in the 110th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Calculate the amount of interest paid over the life of this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Calculate your monthly payments on this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Answer 1 Using present value of annuity formula , we can calculate the monthly loan payment. PV of annuity = P*{[1 - (1+r)^-n]/r} PV of annuity = present value of annuity i.e.Original Loan amount = 85% of $190000 = $1,61,500 P = annuity i.e.monthly loan payment = ? r = rate of interest per month = 4.25% /12 = 0.003542 n = no.of months = 15 year * 12 = 180 161500 = P*{[1 - (1+0.003542)^-180]/0.003542} 161500 = P* 132.9295 P = 1214.93 Monthly payments on this mortgage = $1214.93 Answer 2 Using present value of annuity formula , we can calculate the remaining loan balance after 24th loan payment PV of annuity = P*{[1 - (1+r)^-n]/r} PV of annuity = present value of annuity i.e.loan balance after 24th loan payment = ? P = annuity i.e.monthly loan payment = 1214.93 r = rate of interest per month = 4.25% /12 = 0.003542 n = no.of months remaining = 180 - 24 = 156 PV of annuity = 1214.93*{[1 - (1+0.003542)^-156]/0.003542} PV of annuity = 1214.93*119.6975 PV of annuity = 145424.07 Loan balance after 24th loan payment = $145424.07 Amount of interest in 25th payment = Loan balance after 24th payment * Monthly interest rate = $145424.07 * 0.003542 = $515.04 Amount of Principal in 25th payment = Monthly loan payment - Interest in 25th payment = $1214.93 - $515.04 = $699.89 Answer 3 Using present value of annuity formula , we can calculate the remaining loan balance after 109th loan payment PV of annuity = P*{[1 - (1+r)^-n]/r} PV of annuity = present value of annuity i.e.loan balance after 24th loan payment = ? P = annuity i.e.monthly loan payment = 1214.93 r = rate of interest per month = 4.25% /12 = 0.003542 n = no.of months remaining = 180 - 109 = 71 PV of annuity = 1214.93*{[1 - (1+0.003542)^-71]/0.003542} PV of annuity = 1214.93*62.67913 PV of annuity = 76150.73 Loan balance after 24th loan payment = $76150.73 Amount of interest in 110th payment = Loan balance after 109th payment * Monthly interest rate = $76150.73 * 0.003542 = $269.70 Amount of Principal in 110th payment = Monthly loan payment - Interest in 110th payment = $1214.93 - $269.70 = $945.23 Answer 4 The amount of interest paid over the life of this mortgage = Total Loan payment - Loan Original balance = (180 months * $1214.93) - $161500 = $57,187.40

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.