Final answer:
Tom Allan paid $150 in total for 3 Series EE savings bonds, each with a face value of $100. When interest rates increase, the cost of existing bonds with lower rates typically decreases, indicating you would pay less for a bond with a lower interest rate than the current market rate.
Step-by-step explanation:
Tom Allan purchased 3 Series EE savings bonds, each with a face value of $100. Since Series EE savings bonds are usually sold at half their face value, Tom would have paid $50 for each bond. Therefore, the total cost for the 3 bonds would be 3 x $50, which equals $150. Thus, Tom paid $150 in total for the bonds.
Regarding changes in interest rates and the cost of bonds, typically when interest rates rise, the existing bonds with lower interest rates become less attractive, resulting in their market value decreasing. Conversely, if interest rates fall, the value of existing bonds with higher rates increases.
Therefore, if interest rates rise, you would likely pay less than the face value of a bond, like the described $10,000 ten-year bond at 6% interest rate, especially if you are buying it when interest rates are at 9%.
To calculate what you might be willing to pay for such a bond a year before its maturity, you would discount the bond's future payments by the current market interest rate.
For example, if the bond were to pay $10,000 at the end of the year, and the market interest rate is 9%, you would calculate the present value of that $10,000 as follows: PV = FV / (1 + r)^n, where PV is present value, FV is future value ($10,000), r is the interest rate (0.09), and n is the number of periods (1 year).