Final answer:
The purchase price of a $21,000, 9.3% bond, with a yield of 85% compounded semi-annually and maturing in 9 years, is determined by calculating the present value of semi-annual interest payments and the face value of the bond, all discounted at the yield rate. This involves semi-annual interest payments of $976.5 for 18 periods, discounted by the yield rate of 42.5% for the same number of periods.
Step-by-step explanation:
To calculate the purchase price of a $21,000, 9.3% bond yielding 85% compounded semi-annually, we need to consider both the interest payments and the principal repayment at maturity, discounted at the yield rate. The bond pays semi-annual interest, so the interest payment every six months will be $21,000 times 9.3% divided by 2, which equates to $976.5 per period. There are a total of 18 interest payments remaining since the bond is 9 years away from maturity and interest is paid semi-annually.
We calculate the present value of all semi-annual interest payments and the principal amount using the following formula:
Present Value = C * [(1 - (1 + r)^(-n)) / r] + FV / (1 + r)^n,
where C is the semi-annual interest payment, r is the yield per semi-annual period (42.5%), n is the total number of semi-annual periods left, and FV is the face value of the bond.
Using this formula:
Purchase Price = $976.5 * [(1 - (1 + 0.425)^(-18)) / 0.425] + $21,000 / (1 + 0.425)^18,
After calculating, we round the final answer to the nearest cent.