A $10,000,8%,5-year bond pays fixed interest of $400 every 6 months.If the current market rate of interest is 6%,what is the present value of the bond? (Round to the nearest dollar.)
A) $10,004
B) $10,882
C) $10,852
D) $10,054

Question

Quizplus · Accepted Answer

To compute the present value of the bond, we need to discount the future cash flows (i.e. interest payments and principal repayment) using the current market rate of interest.
Every 6 months, the bond pays an interest of $400, so for 5 years, there will be 10 payments in total:
Year 0: -$10,000 (principal payment)
Year 0.5: $400
Year 1: $400
Year 1.5: $400
Year 2: $400
Year 2.5: $400
Year 3: $400
Year 3.5: $400
Year 4: $400
Year 4.5: $400
Year 5: $10,400 ($10,000 of principal repayment and the last interest payment of $400)
To find the present value, we need to discount each of the 10 cash flows using the current market rate of interest of 6%. We can use the formula:
Present Value = Cash flow / (1 + r)^n
where r is the rate of interest and n is the number of periods. For example, the present value of the first interest payment of $400 received after 6 months is:
Present Value of first interest payment = $400 / (1 + 0.06/2)^1
= $377.36
Similarly, the present value of each of the other 9 cash flows can be computed and then added up to find the total present value of the bond. Using this method, we find that the present value is closest to $10,852, which is answer choice C.

A $10,000,8%,5-Year Bond Pays Fixed Interest of $400 Every 6