Question

Please only answer E, F and G. I need handwritten workings please. NO EXCEL.

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.

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)

Answer 1

Please note we are allowed to answer only first four sub qustions:

a. Effective Monthly rate on the loan

Effective Annual rate = 5%

Let r be the eq. monthly rate

Therefore , (1+r)^12-1 = 0.05

i.e. (1+r)^12 = 1.05

1+r = 12th root of 1.05

i.e. 1+r = 1.004074

Therefore , r = 0.004074 = 0.41%

Effective Monthly Rate = 0.41%

b.First Repayment consists only of interest payments as the first five years are the interest only period

Therefore, First Repayment = 100,000 * 0.41% = 410$

c. Assuming all interest is paid until end of five years loan outstanding at the end of five years is 100,000

Rate = 0.41% per month

Present Value at the end o five years is therefore 100,000

N =No. of periods = 15 years * 12 months = 180

Equivalent Monthly Installment uing annuity formula is calculated as below

EMI = PV * r / [1-(1+r)^-n ]= 100,000*0.41/(1-0.48)= 410/0.52 = 788$.

Please note there is slight rounding off. Actual monthly interest rate = 0.4074%, using that we get EMI of 785$