The face value is $81,000, the stated rate is 10%, and the term of the bond is eight years. The bond pays interest semiannually. At the time of issue, the market rate is 8%. What is the present value of the bond at the market rate? Present value of $1:
4% 5% 6% 7% 8%
15 0.555 0.481 0.417 0.362 0.315
16 0.534 0.458 0.394 0.339 0.292
17 0.513 0.436 0.371 0.317 0.270
18 0.494 0.416 0.350 0.296 0.250
19 0.475 0.396 0.331 0.277 0.232

a. $91,561
b. $47,773
c. $43,673
d. $84,788

The Present Value of the bond at the market rate = $90,438.36  

Explanation:

The value of the bond is the present value(PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).  

Value of Bond = PV of interest + PV of RV  

The value of bond can be worked out as follows:  

Step 1  

PV of interest payments  

Semi annul interest payment  

= 10% × 81000 × 1/2 = 4050

Semi-annual yield = 8%/2= 4 % per six months  

Total period to maturity (in months)  

= (2 × 8) = 16 periods (Note the bond term is 8 yeras)  

PV of interest = 4050 × (1-1.04^(-16))/0.04 = 47,191.79

Step 2  

PV of Redemption Value  

Assuming a redemption value equals to the nominal value =

PV of RV = 81,000 × 1.04^-16 =  43,246.56  

Step 3 :Total Present Value

Total prent value =  43,246.56  + 47,191.79721  =  90,438.36

The Present Value of the bond at the market rate = $90,438.36  

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