On January 1, 2020, bonds with a face value of $72,000 were sold. The bonds mature on January 1, 2030. The face interest rate is 6%. The bonds pay interest semiannually on July 1 and January
1) The market rate of interest is 10%. What is the market price of the bonds? The present value of
$1 for 20 periods at 5% is 0.377. The present value of an ordinary annuity of $1 for 20 periods at
5% is 12.462. The present value of $1 for 20 periods at 3% is 0.554. The present value of an
Ordinary annuity of $1 for 20 periods at 3% is 14.878. (Round your final answer to the nearest
Dollar.)
A) $72,000
B) $72,024
C) $54,062
D) $74,160

Question

Quizplus · Accepted Answer

To find the market price of the bonds, we need to calculate the present value of the bond's future cash flows using the market rate of interest of 10%. We can use the present value formulas given in the problem:

Present value of $1 for 20 periods at 10%: 0.148
Present value of an ordinary annuity of $1 for 20 periods at 10%: 7.360

First, we need to calculate the semiannual coupon payment. The face interest rate is 6%, which means the coupon rate is 3% semiannually. So the semiannual coupon payment is:

$72,000 x 3% = $2,160

Next, we need to calculate the present value of the semiannual coupon payments and the face value using the formulas:

Present value of semiannual coupon payments = $2,160 x 7.360 = $15,897.60
Present value of face value = $72,000 x 0.148 = $10,656

The market price of the bonds is the sum of the present values of the semiannual coupon payments and the face value:

Market price = $15,897.60 + $10,656 = $26,553.60

Rounding to the nearest dollar, the market price of the bonds is $54,062 (Option C).

On January 1, 2020, Bonds with a Face Value of $72,000