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.

1. a) Calculate the equivalent effective monthly rate on the loan. (1 mark)

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

   space (1 mark)

3. c) Calculate the size of the level repayments that occur after the initial 5-year

   interest-only period.

10 years have passed, and Gerald’s business is doing well. Further, he has made all the repayments on his loan so far as described above, and has just made the repayment due today. However, it has just been announced that the interest rate on Gerald’s loan will go up to 5.5% p.a. compounding semi-annually.

4. d) Calculate the new equivalent effective monthly rate on the loan. (1 mark)

5. e) Calculate the current loan outstanding (again, it is 10 years after the loan was initially taken out). Note that the new interest rate only applies from today onwards.
   space

6. f) Because Gerald’s business is doing well, he decides to repay a lump sum of $10,000 immediately. To further reduce the amount of interest he is paying to the bank, he will increase his monthly repayments to $1,000 per month.

   How many full repayments of $1,000 does Gerald have to make in order to fully repay this loan? (Note: Gerald may need to make a further, smaller payment in the subsequent month)

7. g) Calculate the size of the smaller payment. (1 mark)

Answer 1

Hello. As per pur Honor Code, we will provide the answers to the first four parts of this question.

Part(a)

Since it is given in the question that the interest rate is charged 5%p.a. effective. We will convert the given rate to the nominal rate and divide it by 12 to find the effective monthly rate.

we know,   

where EAR= Efeective annual rate

i= nominal rate

n = number of periods.

We may use this formula to compute the nominal rate or use excel function =NOMINAL(effect rate, nper)

We will use the excel to compute the same.

Effective rate	5%
nper	12
Nominal rate	0.048889

In order to determine the monthly rate, we divide the Nominal rate of 4.88% by 12 which gives us 0.406%.

Part(b)

Since the First 5 years repayment is an Interest-only repayment. It will be calculated by multiplying the loan amount with the effective monthly rate that we found out in part (a).

First Repayment= $100,000*0.406% = $406.

Part (c)

We will use Excel to perform the given Repayment calculation.

Loan	100,000
Rate of interest	0.00406
nper	180
Repayment amount	($784.14)

Therefore, the repayment amount will be $784.14 .We used the Function =PMT(rate,nper,PV)

Part (d) Given : Rate of Interest= 5.5% p.a compounding semi-annually.

We will divide the interest rate by 6 to convert it into equivalent effective monthly rate.

Equivalent effective monthly rate= 5.5/6

=.916% or 0.00916