Question

You want to buy a car valued at $48,000. You will make an upfront down-payment of $5,000 on the car, and borrow the rest of the money from your bank. Your bank will give you a 5-year loan at 2.5% APR compounded semi-annually. You plan to make biweekly payments (i.e., one payment every two weeks) on the loan. The bank requires that you make the first payment two weeks after you signed the loan contract. Find the answer to the following questions.

a. What is the effective annual rate?

b. What is the effective biweekly rate?

c. What will be your biweekly loan payment?

d. What is the balance on your loan in 3 years’ time, after 78 payments?

e. Show the amortization schedule (table) for the first 5 payments. If you are doing this on an Excel spreadsheet, copy and paste the first 5 rows from the amortization schedule into a Microsoft Word (or any other word-processing software) document file.

f. You want to put enough money into your bank account to pay for the loan payments for the next six months. If your bank account yields an APR of 2% (compounded bi-weekly), how much money should you put in your bank account now?

Answer 1

Answer (a):

The rate of interest is 2.5% APR compounded semi-annually

Effective annual rate = (1 + 2.5%/2)^2 - 1 = 2.515625%

Effective annual rate = 2.515625%

Answer (b):

Effective biweekly rate = (1 +2.515625%) ^(1/26) - 1 = 0.0956035171988168%

Effective biweekly rate = 0.0956035171988168%

Answer (c):

Loan amount = PV = 48000 - 5000 = $43,000

NPER in biweekly periods = 5 * 26 = 130

Biweekly interest rate = 0.0956035171988168%

Biweekly loan payment = PMT(rate, nper, pv, fv, type) = PMT(0.0956035171988168%, 130, -43000, 0,0) = $351.9075

Biweekly loan payment = $351.91

Answer (d):

Remaning number of biweekly payments after 78 payments = 130 - 78 = 52

Balance on your loan in 3 years’ time, after 78 payments = PV(0.0956035171988168%, 52,-351.9075, 0,0)

=$17,843.46

Balance on your loan in 3 years’ time, after 78 payments = $17,843.46  

Answer (e):

First 5 rows from the amortization schedule are calculated and given below:

Above excel with 'show formula' is as follows:

Answer (f):

Biweely interest rate = 2%/26

Amount of money you need to put in bank account = PV(rate, nper, pmt, fv, type)

= PV(2%/26, 6, -351.9075, 0, 0)

= $2105.77

Amount of money you need to put in bank account = $2,105.77