Question

Belinda purchased a 60-day $200,000 bank bill (at a simple interest rate) on 14 March 2022. The purchase price was $197.000. She sold this bank bill on 22 April 2022.

(a) What was her selling price, if she sold this bank bill at a yield of 3.44% p.a. (simple interest)?
(b) Assume that Belinda sold this bank bill at a price of $197,800 and deposited all sale proceeds into an account to earn a simple interest rate of 2.05% p.a. up to the maturity date of the above bank bill. What is the annualised (simple interest) yield for this 60-day investment?

Answer 1

Belinda's selling price of the bank bill at a yield of 3.44% p.a. would be $197,729.04. Calculating her annualized yield involves combining interest from selling the bill and from the account deposit, then annualizing the sum. To find the yield, use the combined interest over the total period and purchase price.

Step-by-step explanation:

Calculating the Selling Price of a Bank Bill with Simple Interest

To calculate Belinda's selling price of the bank bill at a yield of 3.44% p.a., we need to determine the interest earned during the period she held the bill. She bought the bill on March 14, 2022, and sold it on April 22, 2022.

The number of days Belinda held the bill can be calculated by counting from March 14 to April 22. For simplicity, let's assume each month has 30 days, which equates to 39 days in total for this period.

To find the selling price, we use the formula for simple interest: Interest = Principal × Rate × Time. Here the principal is the face value of the bank bill, which is $200,000, the rate is the yield of 3.44% per annum, and time is the holding period in years (39/365).

Interest = $200,000 × 0.0344 × (39/365) = $729.04

Belinda's selling price would be the purchase price plus the accrued interest: Selling Price = $197,000 + $729.04 = $197,729.04.

Calculating the Annualised Yield on the Combined Investment

If Belinda sold the bank bill at $197,800 and then deposited the proceeds in an account at a simple interest rate of 2.05% p.a., we need to calculate the additional interest earned until the maturity date of the original bank bill (which is 60 days from March 14).

First, we find the interest from the deposit: Interest = $197,800 × 0.0205 × (21/365), which is the period from April 22 to May 13 (assuming a 30 day April).

Then, we combine the total interest from both investments and annualise it to find the yield.

We can use the combined purchase price and selling price to find the yield: Annualised Yield = (Total Interest Earned / Purchase Price) × (365 / Investment Period).

The Investment Period in this case is 60 days, the period from March 14 to May 13.