You purchased a five-year annual payment 6 percent coupon bond for $1,000

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

2 months ago

Solution 1

Guest Guest #2391064
2 months ago

Answer:

B. 5.89 percent

Explanation:

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

Principal \: (1+ r)^{time} = Amount

Principal 1,043.29

time 5.00

rate 0.05000

1043.29 \: (1+ 0.05)^{5} = Amount

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:

Principal \: (1+ r)^{time} = Amount

Principal 1,000

time 5.00

rate              r

1,000 \: (1+ r)^{5} = 1,331.53

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

r = 0.058937166

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