uconn has issued a 10 year $5,000,000 bond with semi annual interest payment with a contract rate of interest of 8%..determine the following
you: how much will uconn have to pay to retire the bonds after it pays off the final interest payment at the end of the 10th year?
To determine how much UConn will have to pay to retire the bonds after it pays off the final interest payment at the end of the 10th year, we need to calculate the face value of the bond and the final interest payment.
First, let's calculate the face value of the bond. The face value is the amount that UConn borrowed and needs to repay at the end of the bond term. In this case, the face value is $5,000,000.
Next, let's calculate the final interest payment. The semi-annual interest payment is based on the contract rate of interest of 8%. Since the payments are semi-annual, the annual interest rate is divided by 2. So the semi-annual interest rate is 8% divided by 2, which is 4%. The number of periods for the bond is 10 years, and since there are two payments per year, the total number of payments is 20.
To calculate the final interest payment, we need to find the present value of the bond's interest payments at the end of the 10th year. Using the formula for present value of an annuity, we can calculate it as follows:
Final interest payment = (Semi-annual interest payment) * (1 - (1 + Semi-annual interest rate)^(-Number of periods)) / Semi-annual interest rate
Plugging in the values, we get:
Final interest payment = (Semi-annual interest payment) * (1 - (1 + 0.04)^(-20)) / 0.04
Now let's calculate the semi-annual interest payment:
Semi-annual interest payment = (Face value) * (Semi-annual interest rate) = $5,000,000 * 0.04
Finally, substituting this value into the equation for the final interest payment, we can calculate it:
Final interest payment = ($5,000,000 * 0.04) * (1 - (1 + 0.04)^(-20)) / 0.04
Solving this equation will give us the value of the final interest payment, which when added to the face value of the bond ($5,000,000) will give us the total amount that UConn will have to pay to retire the bonds after the final interest payment at the end of the 10th year.