Question

Suppose that you plan to borrow $15,000 student loans to attend a university. You are considering borrowing the loan from XYZ. XYZ offers two options for the repayment of your loan. One is the deferred repayment option and the other is interest repayment option. The APR for the deferred repayment option is 3.75% and the APR for the interest repayment option is 3.15%. You plan to finish your undergraduate study in university within five years. The two repayment options are described as below:Deferred repayment option: You make no scheduled student loan payments for 5 years while you are in school and in 1 year of the grace period after you graduate. However, the unpaid interest every month will be added to your principal amount at the end of your grace period. After the grace period, the total amount your will pay will be equal to the principal you borrow and the accumulated unpaid interest. Each month you will be required to pay the same amount, which includes interest and the required principal repayment. You are required to completely pay off your loan within 10 years. Interest repayment option: You pay interest every month when you are in school and in grace period. After the grace period, you will start to pay the principal of the loan. Each month you will be required to pay the same amount, which includes interest and the required principal repayment. You are required to completely pay off your loan within 10 years.

1. Please use Excel to work on the following questions:

1) Set up the loan amortization tables for the loans with these two different repayment options, respectively.

2) How much interest will you pay in total when you pay off your loan offered by these two different repayment options, respectively?

3) How much will you pay in total, including interest and principal, for these two different repayment options, respectively?

Answer 1

Option 1:

Balance at the end of year 6 when repayment starts= P*(1+r)^n

Where

P= Loan amount ($15,000),

r =Interest rate per month= 3.75%/12 = 0.3125%

n= Number of months= 12*6= 72

Balance at the end of 6 years= 15000*(1+0.3125%)^72= $18,778.25

Monthly payments from Month 73 onwards= $187.90

Total interest paid= $7,547.70

Total amount paid= $22,547.70

Details of calculation and amortization schedule (relevant portions only) as below:

Option 2:

Interest is paid at the end of each month

Hence principal at the end of 6 years= $15,000

Monthly payments from month 73 onwards= $145.88

Total payments made= $5,340.84

Total interest paid= $20,340.84

Details of calculation and amortization schedule (relevant portions only) as below: