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A $21,000, 9.3% bond redeemable at par is purchased 9 years before maturity to yield 85% compounded semi-annually, if the bond interest is payable semi-annually, what is the purchase price of the bond?

The purchase price of the band is $ ....
(Round the final answer to the nearest cent as needed Round all intermediate values to six decimal places as needed)

1 Answer

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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.

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