Question

(a) After making payments of $911.10 for 6 years on your 30-year loan at 8.1%, you decide to sell your home. What is the loan payoff? (Round your answer to two decimal places.)

(b) A homeowner has a mortgage payment of $995.10, an annual property tax bill of $592, and an annual fire insurance premium of $280. Find the total monthly payment for the mortgage, property tax, and fire insurance. (Round your answer to the nearest cent.)

(c) Suppose you obtain a 30-year mortgage loan of $193,000 at an annual interest rate of 8.8%. The annual property tax bill is $977 and the annual fire insurance premium is $491. Find the total monthly payment for the mortgage, property tax, and fire insurance. (Round your answer to the nearest cent.)

(d) Leona Jefferson purchased a home and obtained a 20-year loan of $436,000 at an annual interest rate of 6.5%. Find the amount of interest paid on the loan over the 20 years. (Round your answer to the nearest cent.)

(e) Find the mortgage payment for a 15-year loan of $223,700 at an annual interest rate of 8.15%. (Round your answer to two decimal places.)

Answer 1

a]

First, we calculate the original loan amount using PV function in Excel :

rate = 8.1%/12 (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pmt = -911.10 (monthly payment)

PV is calculated to be $122,997.35

Now, we calculate the principal paid off after 6 years (72 months) using CUMPRINC function in Excel :

rate = 8.1%/12 (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 122997.35 (original loan amount)

start period = 1 (We are calculating principal paid off between 1st and 72nd month)

end period = 72 (We are calculating principal paid off between 1st and 72nd month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be $7,465.58

The balance loan principal outstanding after 6 years =  $122,997.35 - $7,465.58 = $115,531.77

b]

Total monthly payment = monthly mortgage payment + monthly tax + monthly insurance

monthly tax = annual tax / 12 = $592 / 12 = $49.33

monthly insurance =  annual insurance / 12 = $280 / 12 = $23.33

Total monthly payment = $995.10 + $49.33 + $23.33 = $1,067.77

c]

Monthly loan payment is calculated using PMT function in Excel :

rate = 8.8% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 193000 (loan amount)

PMT is calculated to be $1,525.23

Total monthly payment = monthly mortgage payment + monthly tax + monthly insurance

monthly tax = annual tax / 12 = $977 / 12 = $81.42

monthly insurance =  annual insurance / 12 = $491 / 12 = $40.92

Total monthly payment = $1,525.23 + $81.42 + $40.92 = $1,647.56

d]

Monthly loan payment is calculated using PMT function in Excel :

rate = 6.5% / 12   (converting annual rate into monthly rate)

nper = 20*12 (20 year loan with 12 monthly payments each year)

pv = 436000 (loan amount)

PMT is calculated to be $3,250.70

Interest paid on loan over 20 years = total payments - loan amount

Interest paid on loan over 20 years = ($3,250.70 * 20 * 12) - $436,000 = $344,167.73