Davis & Davis issued $1000 par value bonds at 102.The bonds pay 12% interest annually and mature in 30 years.The market rate of interest is (round to the nearest hundredth of a percent)[blank].

Question

Quizplus · Accepted Answer

To find the market rate of interest, we need to use the formula for present value of a bond:
PV = C × ((1 - (1 + r)^-n) ÷ r) + M ÷ (1 + r)^n
Where PV is the selling price of the bond (in this case, $1020), C is the coupon payment (in this case, $120), r is the market interest rate (what we're trying to find), n is the number of periods (in this case, 30 years), and M is the maturity value (in this case, $1000).
Plugging in the values yields:
$1020 = $120 x ((1 - (1 + r)^-30) ÷ r) + $1000 ÷ (1 + r)^30
Using trial and error, we find that a market rate of 11.71% results in a present value of $1020. Therefore, the answer is B.

Davis & Davis Issued $1000 Par Value Bonds at 102