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. Using this information, answer the following questions.

a) Calculate the equivalent effective monthly rate on the loan.

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

c) 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%

b.

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

c.

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

so loan balance (P) = 100000

monthly rate =0.004074124

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

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

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

=785.0208241

=785.0208241

so level payment after year 5 will be $785.02