Question

Gerald has taken out a loan of $100,000 today to start a business. He has agreed to repay the loan on the following terms:

• Repayments will be made on a monthly basis. The first repayment will be made exactly one month from today.

• The repayments for the first 5 years will cover interest only to help reduce the financial burden for Gerald’s business at the start.

• After the 5-year interest-only period, Gerald will make level monthly payments that will fully repay the loan after an additional 15 years (i.e. 20 years from today, the loan will be fully repaid).

• The interest charged is 5% p.a. effective.

1) Calculate the size of the first repayment due exactly one month from now.

2) Calculate the size of the level repayments that occur after the initial 5-year interest-only period.

Answer 1

a.

annual effective rate of interest = 5%

effective annual rate = ((1+monthly effective rate)^number of months in year)-1

5% = ((1+i)^12)-1

1+0.05 = (1+i)^12

(1.05)^(1/12) = (1+i)

i = 1.004074124-1

0.004074124

So effective monthly rate is 0.004074124 or 0.4074%

first 5 years only monthly interest will be covered.

monthly interest = loan amount * effective monthly rate

100000*0.004074124

407.4124

So monthly repayment would be $407.41

b.

As for 5 years, interest is paid only. So remaining principal balance as on 6th year beginning will be still $100000

so loan balance (PV) = 100000

monthly rate =0.004074124

number of months repayment in 15 years (n) = 15*12 = 180

Monthly Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)

100000*0.004074124*((1+0.004074124)^180)/(((1+0.004074124)^180)-1)

785.0208241

so level payment after year 5 will be $785.02