Question

Your boss, who never took an engineering economy course, is buying a new house and needs your help in answering some questions. The loan amount will be in the ‘‘jumbo loan’’ category of $600,000 at (1) 6% per year compounded monthly over 30 years, or (2) 5.625% compounded monthly over 15 years. There are no loan initiation fees, points paid, or other charges. Prepayment, if desired, can be done without penalty.

a) What is the monthly payment for plan (1)?

b)What is the monthly payment for plan (2)?

c) What is the total interest paid over the life of loan (1)?

d)What is the total interest paid over the life of loan (2)?

Answer 1

a.

At 6% rate:

Monthly = A =?

Present value = PV = 600,000

r = rate of interest = 0.06

n = Number of years = 30

m = Number of months is a year = 12

PV = {A / (r/m)} {1 – (1 + (r/m))^-(n × m)}

600,000 = {A / (0.06/12)} {1 – (1 + (0.06/12))^-(30 × 12)}

600,000 = (A / 0.005) {1 – (1 + 0.005)^-360}

600,000 × 0.005 = A {1 – (1/1.005^360)}

3000 = A (1 – (1/6.022575))

3000 = A (5.022575 / 6.022575)

A = 3000 × (6.022575 / 5.022575)

A = 3,597.30

Answer: the monthly payment is $3,597.30.

b.

At 5.625% rate:

Monthly = A =?

Present value = PV = 600,000

r = rate of interest = 0.05625

n = Number of years = 15

m = Number of months is a year = 12

PV = {A / (r/m)} {1 – (1 + (r/m))^-(n × m)}

600,000 = {A / (0.05625/12)} {1 – (1 + (0.05625/12))^-(15 × 12)}

600,000 = (A / 0.0046875) {1 – (1 + 0.0046875)^-180}

600,000 × 0.0046875 = A {1 – (1/1.0046875^180)}

2,812.5 = A (1 – (1/2.3204905))

2,812.5 = A (1.3204905 / 2.3204905)

A = 2,812.50 × (2.3204905 / 1.3204905)

A = 4,942.39

Answer: the monthly payment is $4,942.39.

c.

Total payment = A × Number of months

                        = 3,597.30 × 360

                        = 1,295,028

Total interest payment = Total payment – Present value

                                    = 1,295,028 – 600,000

                                    = $695,028 (Answer)

d.

Total payment = A × Number of months

                        = 4,942.39 × 180

                        = 889,630.20

Total interest payment = Total payment – Present value

                                    = 889,630.20 – 600,000

                                    = $289,630.20 (Answer)