You have just purchased a 10-year,$1,000 par value bond.The coupon rate on this bond is 8 percent annually,with interest being paid each 6 months.If you expect to earn a 10 percent simple rate of return on this bond,how much did you pay for it?

Question

Quizplus · Accepted Answer

The bond pays semi-annual interest of $40 (8% of $1,000 divided by 2), and the face value is $1,000. To find the price of the bond given a 10% annual simple interest rate (5% per period since interest is semi-annual), we use the present value formula for an annuity to calculate the present value of the interest payments, plus the present value of the face value. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], and the present value of a lump sum is PV = FV / (1 + r)^n. Here, PMT = $40, r = 0.05 (since 10% annual rate divided by 2 for semi-annual), n = 20 periods (10 years * 2), and FV = $1,000. Plugging these into the formulas gives us the bond's price, which is closest to $875.38.

You Have Just Purchased a 10-Year,$1,000 Par Value Bond