You purchased a 5-year annual-interest coupon bond 1 year ago. Its coupon interest rate was 6%, and its par value was $1,000. At the time you purchased the bond, the yield to maturity was 4%. If you sold the bond after receiving the first interest payment and the bond's yield to maturity had changed to 3%, your annual total rate of return on holding the bond for that year would have been approximately _________.
In order to answer this question, we need to calculate the price of bond - both at the time of purchase and at the time of sale.
Price of a bond is mathematically represented as:
where P is price of a bond with periodic coupon C, periodic YTM i, n periods to maturity and M face value.
C = 6% * $1000 = $60, M = $1000
At the time of purchase, n = 5, i = 4%.
P = 267.1093 + 821.9271
P = 1,089.0364 --> Purchase Price
At the time of purchase, n = 4, i = 3%.
P = 223.0259 + 888.4870
P = 1,111.5130 --> Sale Price
Total Return = (Final Price - Purchase Price + Coupon)/Purchase Price
Total Return = (1111.51 - 1089.04 + 60)/1089.04
Total return = 7.58% But this answer is not in the 4 options mentioned. Are we missing on an option?
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