Zax started a small business selling computers and accessories last year. He took out a loan at the time, and currently owes the bank $398,000. Below is some additional information regarding Zax's loan:

• Zax has been making level monthly repayments on his loan, and will continue to do so. The next payment is due exactly one month from today.
• The bank is charging Zax interest on this loan at 7.3% p.a. effective.

(a) Determine the equivalent effective monthly rate Zax is being charged on his loan. Give your answer as a percentage to 4 decimal places. (1 mark)

(b) Using your answer from part a), calculate the level monthly repayment Zax will need to make in order to repay the loan fully after exactly 20 years. Give your answer to the nearest cent. (1 mark)

C

As a result of the lockdowns, the bank has announced it will immediately lower the interest rate they are charging on loans to help small businesses. They are now charging an effective monthly rate of 0.39% on all loans (including Zax's).

Despite the lockdown, Zax has found that business has actually improved slightly, as more people are buying computers and accessories to set up their home offices. Zax has decided to increase his repayment to $3980 per month starting next month.

(c) How many full payments of $3980 will Zax make under this new arrangement? Keep in mind the bank is now charging a new interest rate, Zax still currently owes $398,000 on the loan, and the first repayment moving forward is exactly one month from today. (1 mark)

(d) The number you calculate in part c) represents the number of FULL re-payments of $3980 that Zax will make on this loan. Which of the following is the most accurate statement we can make about the final extra repayment (if any), without doing any further calculations?

a.

The extra repayment will be smaller than $3980

b.

The extra repayment will be larger than $3980

c.

There will not be any extra repayment required

d.

We cannot say for certain without actually doing the calculation.

(e) Calculate the size of the extra payment made exactly one month after the last full payment of $3980. Give your answer to the nearest cent.

If there is no extra repayment needed, then your answer would be 0.