Respuesta :
Given:
Face value, P = $10000
Time, t = 10 years
Rate, R = 6.4% = 0.064
Let's solve for the following:
• 1) Calculate the semi-annual interest payments.
Apply the formula:
[tex]S=\frac{P\ast R}{2}[/tex]Thus, we have:
[tex]\begin{gathered} S=\frac{10000\ast0.064}{2} \\ \\ S=\frac{640}{2} \\ \\ S=320 \end{gathered}[/tex]The semi-annual interest payment is $320
• (2) Calculate the present value of the payments.
To find the present value, apply the formula:
[tex]PV=\frac{PMT}{r}\ast\lbrack1-\frac{1}{(1+r)^n}\rbrack[/tex]Where:
r = 0.065/2 = 0.0325
n is the number of periods = 10 x 2 = 20
PMT = 320
Thus, we have:
[tex]\begin{gathered} PV=\frac{320}{0.0325}\ast\lbrack1-\frac{1}{(1+0.0325)^{20}}\rbrack \\ \\ PV=9846.15\ast\lbrack1-0.52747\rbrack \\ \\ PV=9846.15\ast0.472529 \\ \\ PV=4652.59 \end{gathered}[/tex]The present value of the payments is $4652.59
3) Calculate the present value of the bond at maturity.
Take the formula:
[tex]PV=\frac{face\text{ value}}{(1+r)^n}[/tex]Thus, we have:
[tex]\begin{gathered} PV=\frac{10000}{(1+0.0325)^{20}} \\ \\ PV=\frac{10000}{1.8958} \\ \\ PV=5274.71 \end{gathered}[/tex]The present value of the bonds at maturity is $5274.71
• 4) Find the price of this bond.
To find the price f this bond, we have:
Price of bond = Present value of payments + Present value at maturity
Price of bond = $4652.59 + $5274.71
Price of bond = $9927.30
The price of this bond is $9,927.30
5) To find the current yield, apply the formula:
[tex]C=\frac{annual\text{ payment}}{\text{current price of bond }}\ast100[/tex]Thus, we have:
[tex]\begin{gathered} \frac{320\ast2}{9927.30}\ast100 \\ \\ =\frac{640}{9927.30}\ast100 \\ \\ =0.0645\ast100 \\ \\ =6.45\text{ \%} \end{gathered}[/tex]The current yield is 6.45%
ANSWER:
1) $320
2) $4,652.59
3) $5,274.71
4) $9,927.30
5) 6.45%
