Question

14. Amortized loans

Your dream is about to come true! You are about to buy your first classic sports car. To do so, you have arranged to borrow 125,000 from your local commercial bank. The interest rate on the loan is 8%. To simplify your calculations, assume that you will repay your loan over the next 5 years by making annual payments at the end of each year. According to the loan officer at the commercial bank, you must answer the following quistions before you can go pick up your new car.

A. How much is the annual payment on your new car loan?

1. 31,307.06 2. 29,115.57 3. 34,437.77 4. 39,133.83

B.How much of your year 2 payment will constitute interest on your loan?

1. 9,124.98 2. 7714.76 3. 10,369.30 4. 8,295.44

C.How much of your year 3 payment will be used to repay principal on loan?

1. 23,112.87 2. 24,852.55 3. 27,337.81 4. 31,065.69

D. How much will you pay in total interest to finance the purchase of your $125,000 car?

1. 31,535.30 2. 39,419.13 3. 29,327.83 4. 34,688.83

Answer 1

A.Annual Payment = Amount of Loan/PVAF(8%, 5 years)

= 125,000/3.993

= $31,307.06

i.e. 1

B.Interest of year 1 = 125,000*8% = $10,000

Principal Amount repaid = $31,307.06 – 10,000 = $21,307.06

Interest in Year 2 = (125,000-21,307.06)*8% = $8,295.44

i.e. 4

C.Principal repaid in Year 2 = 31,307.06-8,295.44 = $23,011.62

Interest Amount of Year 3 = (125,000-21,307.06 – 23,011.62)*8% = $6,464.51

Principal Repaid in Year 3 = 31,307.06 – 6,464.51 = $24,852.55

i.e. 2

D.Total Amount paid = 31,307.06*5 = $156,535.3

Total Interest Amount = $156,535.3 – 125,000

= $31,535.3

i.e. 1.