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You purchased a five-year annual payment 6 percent coupon bond for $1,000 and you planned on holding it to maturity. However, right after you bought the bond, it was called at $1,043.29 when all interest rates fell to 5 percent and remained there for the full five years. You reinvested the money for the full five years. What was your annual compound rate of return off your original investment?

A. 6.00 percent
B. 5.89 percent
C. 5.75 percent
D. 5.23 percent
E. 5.00 percent

Respuesta :

TomShelby

Answer:

B. 5.89 percent

Explanation:

First, we calcualte the amount of the called bond at the 5% rate during 5 years

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 1,043.29

time 5.00

rate 0.05000

[tex]1043.29 \: (1+ 0.05)^{5} = Amount[/tex]

Amount 1,331.53

Now, we invest 1,000 and end up with 1,331.53 after 5 year so we use the same formula of future value of a lump sum to determinate the rate:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 1,000

time 5.00

rate              r

[tex]1,000 \: (1+ r)^{5} = 1,331.53[/tex]

[tex]r = \sqrt[5]{\frac{1331.53}{1000}} -1[/tex]

r = 0.058937166

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