Question

Solve by hand:

Suppose that you bought a 13 week Canadian T-bill at a rate of interest of 0.0345 and face value of $5000. You decide to sell it after 40 days to an investor that expects the rate of interest to be 0.0310. What ROR, in percent, did you earn?

Answer 1

13 weeks equal to 91 days.

Compute the return in 13 weeks using the equation as shown below:

Return = Rate of interest * Number of days / Total days in a year

= 0.0345 * 91 / 365

= 0.00860137

Hence, the return of the bill is 0.00860137.

Compute the price of the bill using the equation as shown below:

Price = Face Value / (1 + Return)

= $5,000 / ( 1 + 0.00860137)

= $4,957.359913

Hence, the price of the bill is $4,957.359913,

After 40 days the number of days remaining of the bill is 51.

Compute the return in 51 days using the equation as shown below:

Return = Rate of interest * Number of days / Total days in a year

= 0.0310 * 51 / 365

= 0.004331507

Hence, the return of the bill is 0.004331507.

Compute the price of the bill using the equation as shown below:

Price = Face Value / (1 + Return)

= $5,000 / ( 1 + 0.004331507)

= $4,978.43587

Hence, the price of the bill is $4,978.43587.

Compute the rate of return using the equation as shown below:

Rate of return = (Sale price - Purchase price) / Purchases price

= ($4,978.43587 - $4,957.359913) / $4,957.359913

= 0.425%

Hence, the rate of return is 0.425%,