Question

A financial analyst draws a cash flow diagram to model the following scenario.

A 90-day commercial bill will mature for $200000. The price paid for the bill at issue was $196041.05. The bill was sold 19 days after issue for $196735.95. Calculate the annual rate of simple interest (as a percentage, to two decimal places) earned by the buyer who paid $196041.05 and sold for $196735.95. What was the annual rate of simple discount (as a percentage, to two decimal places) that the buyer sold at (earning a price of $196735.95)?
Here is the cash flow diagram the analyst drew.
Which response best reflects the values of Z, Y, X, W, V, U, T and S?
a. Z is 90.00, Y is $200000.00, X is $196041.05, W is 19, V is $196735.95, U is not required, T is 8.29% p.a. (simple discount) and S is 6.91% p.a. (simple interest).

Answer 1

To assess the performance of financial transactions, calculations such as simple interest and simple discount are vital, particularly for financial instruments like commercial bills. By applying mathematical formulas to the commercial bill example provided, the annual simple interest and simple discount rates can be derived based on the buy and sell prices and the time frame of the investment.

Step-by-step explanation:

The calculation of simple interest and simple discount represents a real-world scenario that involves evaluating the profitability of financial transactions, specifically with regard to buying and selling financial instruments like commercial bills. The process involves understanding the time value of money and applying mathematical formulas to determine the returns on investment over a period of time. Using the data provided in the question about a commercial bill bought at $196,041.05 and sold for $196,735.95, 19 days later, we can calculate the annual simple interest and simple discount.

The annual rate of simple interest can be calculated by the formula: Simple Interest = (Future Value - Present Value) / (Present Value × (Number of Days / 365)). Using the values provided, you get Simple Interest = (196,735.95 - 196,041.05) / (196,041.05 × (19 / 365)), which will give you the percentage once you do the calculation. The simple discount rate can similarly be computed by seeing how much less the future value is from the matured value of $200,000 when it is discounted for the remaining days (i.e., 90-19 days).