(a) To buy a Treasury bill (T-bill) that matures to $10,000 in 12 months, you must pay $9700. What rate does this earn?
(b) If the bank charges a fee of $20 to buy a T-bill, what is the actual interest rate you earn?
a. P = Po + Po*r*t.
P = $10,000, Po = $9700, t = 1 yr. r = Annual % rate = ?.
b. P = Po + Po*r*t. Po = $9720, All other inputs remain the same. r = ?.
(a) To find the rate at which the T-bill earns, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time)
Given that the T-bill matures to $10,000 in 12 months, and you have to pay $9700 to buy it, we can use the equation:
$10,000 - $9,700 = $9,700 * Rate * 1 year
$300 = $9,700 * Rate
Divide both sides by $9,700 to find the rate:
Rate = $300 / $9,700
Rate = 0.030927 or 3.09%
Therefore, the T-bill earns an annual rate of approximately 3.09%.
(b) To calculate the actual interest rate you earn after deducting the $20 fee, we can modify the equation. The fee is subtracted from the amount you receive at maturity:
$10,000 - $9,700 - $20 = $9,680 * Rate * 1 year
$280 = $9,680 * Rate
Divide both sides by $9,680 to find the rate:
Rate = $280 / $9,680
Rate = 0.02893 or 2.89%
Therefore, after considering the $20 fee, the actual interest rate you earn is approximately 2.89%.
To calculate the rate of return on a Treasury bill (T-bill), we need to use the formula for yield or rate of return. The formula is as follows:
Rate of Return = (Maturity Value - Purchase Price) / Purchase Price
Let's apply this formula to the given scenario:
(a) To buy a T-bill that matures to $10,000 in 12 months, at a purchase price of $9,700, we can calculate the rate of return as follows:
Rate of Return = (10,000 - 9,700) / 9,700
Rate of Return = 300 / 9,700
Rate of Return = 0.0309 or 3.09%
Therefore, the rate of return on the T-bill is 3.09%.
(b) If the bank charges a fee of $20 to buy the T-bill, we need to subtract this fee from the initial investment to get the actual purchase price. Let's recalculate the rate of return:
Actual Purchase Price = Purchase Price - Fee
Actual Purchase Price = 9,700 - 20
Actual Purchase Price = 9,680
Rate of Return = (10,000 - 9,680) / 9,680
Rate of Return = 320 / 9,680
Rate of Return = 0.0331 or 3.31%
Therefore, considering the fee, the actual rate of return on the T-bill is 3.31%.