Question
In: Finance
Alice is concerned about the financing of a home. She saw a home selling for $120,000....
Alice is concerned about the financing of a home. She saw a home selling for $120,000. If she puts 10% down, what will her monthly payment be for a 30 year loan at the following percentages? What is the total cost of interest over the life of the loan for each assumption A, B, C, and D?
A. 8% B. 9% C. 10% D. 11%
Solutions
Expert Solution
| Answer A | |||||||||
| Calculation of monthly payment on loan and total interest over the life of loan when Interest rate is 8% | |||||||||
| We can use the present value of annuity formula to calculate monthly loan payment. | |||||||||
| Present Value of annuity = P x {[1-(1+r)^-n]/r} | |||||||||
| Present Value of annuity = Loan amount = Cost of house x 90% = $120000 x 90% = $108000 | |||||||||
| P = monthly loan payment = ? | |||||||||
| r = interest rate per month = | 0.0067 | ||||||||
| n = number of monthly payments = | 360 | ||||||||
| 108000 = P x {[1-(1+0.0067)^-360]/0.0067} | |||||||||
| 108000 = P x 136.2835 | |||||||||
| P = 792.47 | |||||||||
| Monthly Loan payment = $792.47 | |||||||||
| Total Interest over the life of loan = (Monthly Payment x Number of months) - Loan amount | |||||||||
| Total Interest over the life of loan = ($792.47 x 360) - $108000 | |||||||||
| Total Interest over the life of loan = $1,77,287.67 | |||||||||
| Answer B | |||||||||
| Calculation of monthly payment on loan and total interest over the life of loan when Interest rate is 9% | |||||||||
| We can use the present value of annuity formula to calculate monthly loan payment. | |||||||||
| Present Value of annuity = P x {[1-(1+r)^-n]/r} | |||||||||
| Present Value of annuity = Loan amount = Cost of house x 90% = $120000 x 90% = $108000 | |||||||||
| P = monthly loan payment = ? | |||||||||
| r = interest rate per month = | 0.0075 | ||||||||
| n = number of monthly payments = | 360 | ||||||||
| 108000 = P x {[1-(1+0.0075)^-360]/0.0075} | |||||||||
| 108000 = P x 124.2819 | |||||||||
| P = 868.99 | |||||||||
| Monthly Loan payment = $868.99 | |||||||||
| Total Interest over the life of loan = (Monthly Payment x Number of months) - Loan amount | |||||||||
| Total Interest over the life of loan = ($868.99 x 360) - $108000 | |||||||||
| Total Interest over the life of loan = $2,04,837.27 | |||||||||
| Answer C | |||||||||
| Calculation of monthly payment on loan and total interest over the life of loan when Interest rate is 10% | |||||||||
| We can use the present value of annuity formula to calculate monthly loan payment. | |||||||||
| Present Value of annuity = P x {[1-(1+r)^-n]/r} | |||||||||
| Present Value of annuity = Loan amount = Cost of house x 90% = $120000 x 90% = $108000 | |||||||||
| P = monthly loan payment = ? | |||||||||
| r = interest rate per month = | 0.0083 | ||||||||
| n = number of monthly payments = | 360 | ||||||||
| 108000 = P x {[1-(1+0.0083)^-360]/0.0083} | |||||||||
| 108000 = P x 113.9508 | |||||||||
| P = 947.78 | |||||||||
| Monthly Loan payment = $947.78 | |||||||||
| Total Interest over the life of loan = (Monthly Payment x Number of months) - Loan amount | |||||||||
| Total Interest over the life of loan = ($947.78 x 360) - $108000 | |||||||||
| Total Interest over the life of loan = $2,33,199.83 | |||||||||
| Answer D | |||||||||
| Calculation of monthly payment on loan and total interest over the life of loan when Interest rate is 11% | |||||||||
| We can use the present value of annuity formula to calculate monthly loan payment. | |||||||||
| Present Value of annuity = P x {[1-(1+r)^-n]/r} | |||||||||
| Present Value of annuity = Loan amount = Cost of house x 90% = $120000 x 90% = $108000 | |||||||||
| P = monthly loan payment = ? | |||||||||
| r = interest rate per month = | 0.0092 | ||||||||
| n = number of monthly payments = | 360 | ||||||||
| 108000 = P x {[1-(1+0.0092)^-360]/0.0092} | |||||||||
| 108000 = P x 105.0063 | |||||||||
| P = 1028.51 | |||||||||
| Monthly Loan payment = $1,028.51 | |||||||||
| Total Interest over the life of loan = (Monthly Payment x Number of months) - Loan amount | |||||||||
| Total Interest over the life of loan = ($1028.51 x 360) - $108000 | |||||||||
| Total Interest over the life of loan = $2,62,263.34 | |||||||||
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