Question

A three-month bill is issued at a discount of 5% and the price of a three-month bill is 100 − (3/12) × 5 = 98.75. Therefore, for every $98.75 that you invest today, you receive $100 at the end of three months. The return over three months is 1.25/98.75 = .0127, or 1.27%. This is equivalent to an annual yield of 5.16%. Suppose that one month has passed and the investment still offers the same annually compounded return.

a. Calculate the current price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Current price            $

Answer 1

The bill was issued four months earlier at a discount rate and was priced at 98.75%. Since then, the price of bill earned return of 1.27% in three years and price after three months of issuance was $100. It has been a month after the price was $100.

If the same rate of return is applied to the price of $100 at a monthly rate, we will get the current price of the bill. The rate of return was 1.27% for 3 months, 5.06% for 12 months, so it will be (1.27%/3 = 5.06%/12 = 0.42% per month)

The formula for finding the future value of an amount after a year, following formula will be used:

Future value =P*(1+r)n

here, Pis the amount at time, t=0 ris an annual rate of interest rate n is the number of years

For finding the future value of an amount after a month, we will need to use an interest rate applicable per month. This is obtained by dividing the annual interest rate by 12. In current example, the interest rate per month is 0.42%

We can apply this rate of return to $100 price of bill and get the current price of bill. This value will be:

Price of bill today (i.e. after 4 months of issuance) = 98.75%*(1+0.42%)^4 = $100.42

OR

can be calculated using $100 price at 3rd month = 100%(1 + 0.42%) = $100.42

Both the calculations will give the same result.