Mackenzie purchased a 60-day $200 000 bank bill (at simple interest) on 14 March 2023. The purchase price was $197 000. She sold this bank bill on 22 April 2023.
(b) Assume that Mackenzie sold this bank bill at a price of $197 800 and deposited all sale proceeds into an account to earn simple interest of 2.81% p.a. What is her annualised (simple interest) yield on her 60-day investment from 14 March 2023? Give your answer as a decimal (to five places).
Investing in bank bills is a common practice for individuals seeking relatively low-risk investment opportunities. These short-term debt securities offer a fixed interest rate over a specific period. This essay aims to explain how Mackenzie’s investment in a 60-day $200,000 bank bill, her subsequent sale of the bank bill, and the deposit of the sale proceeds into an account with a 2.81% p.a. interest rate can be used to calculate her annualized simple interest yield.
Initial Investment: On 14 March 2023, Mackenzie purchased a 60-day $200,000 bank bill at a price of $197,000. This initial investment reflects her confidence in the bank bill’s reliability and the offered interest rate.
Selling the Bank Bill: On 22 April 2023, Mackenzie sold the bank bill for $197,800. This sale price indicates her decision to divest the investment before its maturity date, possibly due to changing financial circumstances or investment strategies.
Deposit and Interest Rate: Mackenzie then deposited the sale proceeds of $197,800 into an account that earns a simple interest rate of 2.81% p.a. This choice demonstrates her intention to continue earning interest on her investment without assuming the risk associated with holding the bank bill until maturity.
Calculating Annualized Yield: To calculate the annualized simple interest yield on Mackenzie’s 60-day investment, we can follow these steps:
Determine the interest earned from the bank bill investment: Interest = Selling Price – Purchase Price Interest = $197,800 – $197,000 = $800
Calculate the interest earned during the 60-day investment period: Interest for 60 days = (Interest * 365) / (Purchase Price * Number of Days) Interest for 60 days = ($800 * 365) / ($197,000 * 60) ≈ 0.0692
Convert the 60-day interest to an annualized interest rate: Annualized Interest Rate = (Interest for 60 days / 60 days) * 365 days Annualized Interest Rate = 0.0692 * 365 ≈ 25.24%
Adjust the annualized interest rate to the given 2.81% p.a. interest rate: Annualized Yield = Annualized Interest Rate / Account Interest Rate Annualized Yield = 25.24% / 2.81% ≈ 8.9882
Mackenzie’s annualized simple interest yield on her 60-day bank bill investment, considering the subsequent deposit into an account with a 2.81% p.a. interest rate, is approximately 8.9882 or 0.089882 as a decimal.
This analysis highlights Mackenzie’s financial decision-making process, from purchasing the bank bill to selling it and subsequently depositing the sale proceeds into an interest-bearing account. The calculated annualized yield provides a quantitative measure of the returns generated from her investment strategy.
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