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postnew [5]
3 years ago
12

A $7,500 face value, 20-year bond has a nominal annual coupon rate of 7.4%, paid semiannually. The yield to maturity is 5.3% con

vertible semiannually. In the 4th coupon payment, the amount for amortization of premium is $28.31. Find the redemption amount of the bond.
Business
1 answer:
Stolb23 [73]3 years ago
3 0

Answer:

$134,000

Explanation:

Annual yield (%) = Face value - Purchase value/Face value X 360 X 100%/Maturiy(in days)

Let x be purchase value

2 X 5.3% = $7,500 - x/$7,500 X 360 X 100%/365

100($7,500 - x) = 10.6 X $7,500

$750,000 - 100x = $79,500

100x = $(750,000 - 79,500) = $670,500

x = $6,750

The value of bond for 20-year: 20 X $6,750 = $134,000

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You need to use the formula to calculate the future value of a constant annual deposit:

      Future\text{ }value=Deposit\times \bigg[\dfrac{(1+r)^n-1}{r}\bigg]

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<em><u>1. For a deposit of  $30,800 at the end of each year for the next 11 years, with 7% interest.</u></em>

You will have saved:

         Future\text{ }value=\$ 30,800\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg]

         Future\text{ }value=\$ 30,800\times 15.7835993=\$486,134.86

<em><u>2.  For a deposit of $33,300 each year, for the same number of years and with the same interest rate.</u></em>

You will have saved:

       Future\text{ }value=\$ 33,300\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg]

      Future\text{ }value=\$ 33,300\times 15.7835993=\$525,593.86

<em><u>3. For a deposit of $30,800 each year, but with 11 percent interest, for 11 years.</u></em>

        Future\text{ }value=\$ 30,800\times \bigg[\dfrac{(1+0.11)^{11}-1}{0.11}\bigg]

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Answer:

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