Question

Assume that you have purchased a new home and arranged for a mortgage in the amount of $125,000. The loan is at 4.75% over 15 years.

a. What is your monthly payment?

b. How much of the loan's principal will you pay over the first year of the loan?

c. How much total interest will you pay over years 9 through 11?

d. What will be your loan balance after 14 years?

e. What is the effective rate on your loan?

Answer 1

a.

Loan Amount = $125,000

Interest Rate = 4.75%

Time Period = 15 years

Calculating Monthly Payment,

PMT = [PV = 125,000, FV = 0, T = 180, I = 0.0475/12]

PMT = $972.29

b.

Value of Loan at the end of Year 1,

PV = [FV = 125000, T = 12, PMT = 972.29, I = 0.0475]

PV(end of Year 1) = $119,143.61

Principal paid in Year 1 = 125,000 - 119,143.61

Principal paid in Year 1 = $5,856.39

c.

First Calculating Loan value at the end of Year 9 and Year 11

PV(Year 9) = [FV = 125000, PMt = -972.29, T = 108, I = 0.0475]

PV(Year 9) = $60,809.06

PV(Year 11) = [FV = 125000, PMt = -972.29, T = 132, I = 0.0475]

PV(Year 11) = $42,428.01

Principal paid between Year 9 an Year 11 = 60809.06 - 42428.01

Principal paid between Year 9 an Year 11 = $18,381.05

Total amount paid between Year 9 an Year 11 = 24(972.29)

Total amount paid between Year 9 an Year 11 = $23,334.96

Total interest paid between Year 9 and Year 11 = 23,334.96 - 18,381.05

Total interest paid between Year 9 and Year 11 = $4,953.91

d.

Value fo loan at the end of Year 14,

PV(Year 14) = [FV = 125,000, T = 168, PMT = 972.29, I = 0.0475]

PV(Year 14) = $11,372.72

e.

Effective Rate of Return = (1 + 0.0475/12)¹² - 1

Effective Rate of Return = 4.85%