Freddie decides to buy the fleet of vehicles after all, for a price of 394,000. Freddie's friend Kiki, who is an executive at "Mercury Bank" has arranged a special Interest rate of 24% pa. compounding monthly for Freddie to take out a loan for this purchase. Freddie is considering taking this special offer, and intends to fully repay the loan using level monthly repayments over the coming 8 years. The first payment is exactly one (a) Calculate the size of the level monthly repayment. Give your answer in dollars, to the nearest cent (1 mark) month from today Answer: (b) What is Freddie's loan outstanding after 1 year? Give your answer in dollars, to the nearest cent. (1 mark) Answer: (c) Calculate the interest Freddie is charged in the first year. Give your answer in dollars, to the nearest cent. (1 mark) Answer: (d) Suppose Freddle was charged a higher interest rate for the loan than what kiki had arranged. Assuming Freddie is still borrowing the same amount and making level repayments over 8 years at the same points in time (but a different amount due to the different interest rate), which of the following statements about the total interest Freddie pays in the first year is true? a. The total interest in the first year wil be lower than the answer in parte), as the higher monthly repayments will pay at the principal sooner, meaning less interest is charged b. The total interest in the first year will be higher than the answer in parte), as the interest rate is higher and nothing else about the loan has changed (apart from the repayments) c. The total interest in the first year will be exactly equal to the answer in part c), as the increase in the repayments will compensate any extra interest charged d. We cannot determine anything about the interest in the first year without knowing the exact interest rate and performing a calculation Kik has returned to her office at Mercury Bank, and sees some loan case files have been left for her to review. Alt doans at Mercury Bank charge a fixed interest rate (la. It does not change over the life of the loan), but different loans can have different interest rates charged She reads through these case files and notes the following interesting cases: Case 1: A loan of $493,000 was made with a term of 30 years. There are level monthly repayments of $22077036125, but the interest rate being charged on the loan is not known. Calculate the interest rate for this loan, expressed as an effective monthly rate. Give your answer as a percentage, to 4 decimal places. (1 mark) Answer: Case 2: A loan was made to a customer some time ago, but there are no records of when this occurred, or the original loan amount. All that is known is that exactly one year ago, the loan outstanding was $890,000, there were level monthly repayments of $33063.47681 (the most recent payment being made today), and the loan outstanding today is $530,000 (after taking into account the payment made today). Calculate the interest rate for this loan, expressed as a nominat annual rate compounding monthly. Give your answer as a percentage, to 4 decimal places. (1 mark) Answer: Case 3: A loan of $391,000 was made today by a new customer. The customer has decided to make quarterly repayments of $20527 at the start of each quarter for the forseeable future, After 1 year, the loan outstanding turns out to be $386030.493926 (note that only 4 repayments are made). Calculate the interest rate for this loan, expressed as a nominal annual rate compounding quarterly. Give your answer as a percentage, to 4 decimal places. (mark)
