Final answer:
The question is about financial mathematics assessing the value of a bond when interest rates change. A bond with a set coupon rate will decrease in price if market interest rates rise. Thus, a $10,000 bond at 6% would be worth less when market rates are at 9%.
Step-by-step explanation:
The subject of the question falls within the area of Mathematics, specifically in financial mathematics dealing with the valuation of bonds and annuities. Referring to the question concerning purchasing a bond one year before the end of its ten-year term when the interest rates have risen from 6% to 9%, we can deduce that the bond's price would be lower than its face value. This is because the current yield required by the market exceeds the bond's coupon rate. As such, the bond must be discounted to offer a competitive yield.
Example of Bond Valuation
Likewise, if you consider a $10,000 ten-year bond with a 6% interest rate but are looking to buy the bond when the market interest rate is 9%, the calculation would be:
- PV = C / (1+r) + C / (1+r)^2 + ... + C / (1+r)^n + M / (1+r)^n
- Where PV is the present value of the bond, C is the annual coupon payment, r is the market interest rate, and M is the maturity value of the bond.
Because the coupon rate is lower than the market rate, the present value of both the coupon payments and the maturity value will be less than their face values, leading to the bond being valued at less than $10,000.