A $15,000 T-bill is purchased at a 3.85% discount rate for 16 weeks. Find (a) the purchase price of the T-bill, (b) the maturity value, (c) the interest earned, (d) the effective rate of interest to the nearest hundredth of a percent.
To find the answers to the given questions, we can follow these steps:
Step 1: Determine the purchase price of the T-bill:
The T-bill was purchased at a discount rate of 3.85%. The purchase price is calculated by subtracting the discount from the face value of the T-bill.
The formula to calculate the purchase price is:
Purchase Price = Face Value - Discount
In this case, the face value of the T-bill is $15,000. So, the purchase price is calculated as follows:
Purchase Price = $15,000 - (3.85% * $15,000)
Step 2: Calculate the maturity value:
The maturity value of a T-bill is equal to the face value. In this case, the face value is $15,000.
Step 3: Calculate the interest earned:
The interest earned on a T-bill is calculated by subtracting the purchase price from the maturity value.
The formula for calculating the interest earned is:
Interest Earned = Maturity Value - Purchase Price
Step 4: Calculate the effective rate of interest:
The effective rate of interest is the annualized rate of return on the investment. Since the T-bill's holding period is 16 weeks, we need to convert it to a yearly basis.
The formula to calculate the effective rate of interest is:
Effective Rate of Interest = ((Maturity Value - Purchase Price) / Purchase Price) * (52 / Holding Period)
Where Holding Period represents the number of weeks the T-bill is held.
Now let's calculate the answers to the given questions:
(a) Purchase Price:
Purchase Price = $15,000 - (3.85% * $15,000)
(b) Maturity Value:
Maturity Value = $15,000
(c) Interest Earned:
Interest Earned = Maturity Value - Purchase Price
(d) Effective Rate of Interest:
Effective Rate of Interest = ((Maturity Value - Purchase Price) / Purchase Price) * (52 / Holding Period)
Note: In this case, the Holding Period is given as 16 weeks.