Final answer:
The price of a bond is determined by discounting its future cash flows, which include semiannual interest payments and face value, at the market yield rate. To find the total value of 50 bonds, multiply the price of one bond by 50.
Step-by-step explanation:
The question deals with the calculation of the price of a bond and the total value of a set of 50 bonds, given a certain coupon rate, market yield rate, and maturity period. With the bond paying semiannual interest and having a different yield (market rate) than its coupon rate, we need to find the present value of the bond's cash flows to determine its price.
Price of a Bond Calculation
To calculate the price of a bond, we have to discount the bond's future cash flows, which include semiannual interest payments and the face value repaid at maturity, at the market yield rate. The formula to calculate the price of a bond is the present value of an annuity (for the interest payments) plus the present value of a lump sum (for the face value).
Total Value of 50 Bonds
Once the price of one bond is calculated, we multiply that by the number of bonds to get the total investment value. This reflects the total current market price of the investment in these 50 bonds. Due to variations in market interest rates, the price of a bond can be more or less than its face value.