Question

Eric is interested in buying a house for $222,000, and he has the option of a 15-year fixed-rate mortgage or a 30-year fixed-rate mortgage. The interest rate on both of the mortgages is 4.6%. Eric wants to know how much money the 15-year mortgage would save him over the long run. Calculate the amount for Eric by answering the following questions. (5 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point; Part V - 1 point)

Part I: What would Eric's monthly payment be if he chooses the 15-year mortgage?

Part II: What would Eric's monthly payment be if he chooses the 30-year mortgage?


Part III: If Eric chooses the 15-year mortgage, what will be his total cost?

Answer 1

Part I: Monthly payments for 15-year mortgage
P = L[i(1+i)^n]/[(1+i)^n-1]

Where, P = Monthly payments, i = monthly interest rate, n = number of months over which the loan will be paid, L = Mortgage loan.

Substituting;
P = 222,000[0.046/12(1+0.046/12)^15*12]/[(1+0.046/12)^15*12-1] = $1,709.65

Part II: Monthly payment for 30-year mortgage
Using the same formula as above with different number of years,
P = 222,000[0.046/12(1+0.046/12)^30*12]/[(1+0.046/12)^30*12-1] = $1,138.07

Part III: Total coast for 15-year mortgage
Monthly payment = $1,709.65
Total payment (or cost) = 1,709.65*15*12 = $307,737