Question

Question 1 (25 marks/ Time Value of Money)
You are considering taking out a loan from the so-called “Tiger B. Shark” finance company. The company’s leaflet states that the loan you plan to take will be settled on a “four-for-five” weekly basis. You ask your friend, who works in the banking industry, for advice on the following issues related to the loan.

(a) What is the weekly interest rate charged on the loan as implied by the phrase “four-for-five weekly basis” in the leaflet?

(b) What is the effective yearly rate of this loan? Assume that each year has exactly 52 weeks. (The final answer should be rounded to two decimal places in percentage.)          

(c) Suppose you plan to borrow $10,000 under the terms set out in the leaflet for one year (counted as 52 weeks according to the loan contract).

(i) If you make no interest or principal repayments during the period, how much will you have to repay in 52 weeks and how much interest in total will you have to pay for the loan? [Note: Round the final answer to an integer.]

(ii) If you pay interest every week (but make no principal repayment), how much interest in total will you have to pay to the finance company?

(iii) Suppose the finance company allows you to repay the loan over a one-year period with weekly payments. [Note: How many payments will you have to make to pay off the loan in exactly one year?]

- How much will the weekly payment be? Assume the first payment starts today.          
- How much interest in total (direct and indirect) will you have to pay for the loan?
[Note: Round the final answer to an integer.]

Answer 1

(a)

“four-for-five weekly basis” means that for every $4 borrowed, $5 has to be repaid after 1 week.

Weekly interest rate = (amount repaid - amount borrowed) / amount borrowed

Weekly interest rate = ($5 - $4) / $4 = 25%

(b)

Effective yearly rate = (1 + weekly rate)^{number of weeks in 1 year} - 1

Effective yearly rate = (1 + 25%)⁵² - 1

Effective yearly rate = 10947544.25%

(c)

(i)

Interest amount = amount borrowed * (1 + effective yearly rate)

Interest amount = $10,000 * (1 + 10947544.25%)

Interest amount = $1,094,754,25

Amount to repay = amount borrowed + interest = $10,000 + $1,094,754,25 = $1,094,764,425

(ii)

Total interest paid = amount borrowed * weekly interest rate * number of weeks in 1 year

Total interest paid = $10,000 * 25% * 52 = $130,000