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. (1 mark)

b) Calculate the size of the first repayment due exactly one month from now. space (1 mark)

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.

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

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

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)

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

note: please use hand calculations

Answer 1

Answer,

Gerald has taken 100,000 $ as loan. Intially for five years he pays only interest after which he starts paying out the whole loan. BAsed on the information and as per your request to solve the question by hand. Please find answer below:

Part A & B

Part C

Part D

In part D we will first understand the concept of APR and APY and then answer the question so that you can have a better understanding.

APR is the simple interest rate of the period of time.

Whereas APY describes the rate with effects of compounding.

If the compounding is on annual basis both APR and APY are equal however for semi-annual or quarterly compounding these become different.

In above question APR for the year = 5.5%

We will first calculate APY

Thus, the effective monthly rate is 0.453%

Part E

this part of the question is the most complicated especially when solved without excel. We need to calculate how much is left to be paid at the end of 10th year. For this we will use concepts of Present value (PV) and future value (FV).

The solution is as:

As shown the outstanding amount at the end of 10th year is 74,394$.

Part f and g

In this we are given that the annuity is 1000$. Also an upfront payment of 10,000$ has been done. We need to find the time to pay off the whole loan. Again using the PV formula.