URGENTLY NEED HELP FOR THE FOLLOWING QUESTIONS:
1) A $112,000, 90-day commercial paper certificate issued by Bell Canada Enterprises was sold on its issue date for $110,100.
What annual rate of return will it yield to the buyer?
2) A $25,700, 91-day Province of Newfoundland Treasury bill was originally purchased at a price that would yield the investor a 5.438% rate of return if the T-bill is held until maturity. Thirty-four days later, the investor sold the T-bill through his broker for $25,575.
a. What price did the original investor pay for the T-bill? (Do not round the intermediate calculations. Round your answer to the nearest cent.)
Price $
b. What rate of return did the first investor realize during his holding period? (Do not round the intermediate calculations. Round your answer to three decimal places.)
Rate of return
%
c. If the broker sells the t-bill to a second investor for $25,575, what rate of return will the second investor realize if he or she holds the t-bill until maturity? (Do not round the intermediate calculations. Round your answer to three decimal places.)
Rate of return
%
3) Suppose that the current rates on 180- and 360-day GICs are 1.25% and 1.50%, respectively. An investor is weighing the alternatives of purchasing a 360-day GIC versus purchasing a 180-day GIC and then reinvesting its maturity value in a second 180-day GIC. What would the interest rate on 180-day GICs have to be 180 days from now for the investor to end up in the same financial position with either alternative?
4) You buy a house from your brother and promise to pay him the $25,000 down payment in 2 years with 1.25% simple interest. You decide to pay off the down payment early, in one year. What amount will settle the debt if money can earn 0.75%?
Here are the solutions to the questions you've posted:
1) To find the annual rate of return on the commercial paper certificate, use the formula for Simple Yield:
Rate of Return = (Face Value - Purchase Price) / Purchase Price * (365 / Number of Days)
In this case, the face value is $112,000, the purchase price is $110,100, and the number of days is 90.
Rate of Return = ($112,000 - $110,100) / $110,100 * (365 / 90)
2)
a) To find the price the original investor paid for the T-bill, use the formula for Present Value (PV):
PV = FV / (1 + r)^n
In this case, the face value is $25,700, the rate of return is 5.438%, the holding period is 91 days, and the sale price is $25,575.
Plug in the values to find the price paid by the original investor.
b) To find the rate of return realized by the first investor, use the formula:
Rate of Return = (Sale Price - Purchase Price) / Purchase Price * (365 / Holding Period)
In this case, the purchase price is the answer from part (a), the sale price is $25,575, and the holding period is 34 days.
c) To find the rate of return for the second investor, we can use the same formula as in part (b).
Rate of Return = (Sale Price - Purchase Price) / Purchase Price * (365 / Holding Period)
In this case, the purchase price is $25,575, the sale price is also $25,575, and the holding period is 91 days.
3) To find the interest rate on 180-day GICs 180 days from now, we need to equate the future value of investing in a 360-day GIC to the combined future value of investing in two consecutive 180-day GICs.
Use the formula for Future Value (FV):
FV = PV * (1 + r)^n
Let's assume the PV for both options is $1,000.
For the first option (360-day GIC), the rate is 1.50% with a holding period of 360 days.
For the second option (180-day GICs), the rate is unknown, with a holding period of 180 days.
Set up the equation:
$1,000 * (1 + 0.015)^360 = $1,000 * (1 + r)^180 * (1 + r)^180
Solve for r, the interest rate on the 180-day GICs 180 days from now.
4) To find the amount that will settle the debt if it is paid off in one year, we'll use the formula for Simple Interest:
Interest = Principal * Rate * Time
In this case, the principal (or down payment) is $25,000, the rate is 1.25%, and the time is 1 year.
Find the interest owed and subtract it from the principal to find the final amount to settle the debt.
Next, to calculate the amount if money can earn 0.75%, we need to use the formula for Future Value (FV):
FV = PV * (1 + r)^t
In this case, the present value (PV) is the new amount to settle the debt, the rate (r) is 0.75%, and the time (t) is 1 year.
Find the future value to know the final amount needed to settle the debt.
I hope these explanations help you to solve the questions.