The sum of $1, 000 is invested in five-year bonds with face value $100 and $8 coupons paid annually. All coupons are reinvested in bonds of the same kind. Assuming that the bonds are trading at par and the interest rate remains constant throughout the period to maturity, compute the number of bonds

Question

The sum of $1, 000 is invested in five-year bonds with face value $100 and $8 coupons paid annually. All coupons are reinvested in bonds of the same kind. Assuming that the bonds are trading at par and the interest rate remains constant throughout the period to maturity, compute the number of bonds held during each consecutive year of the investment.

Accepted Answer

Because the bond is trading at par and the interest rates remain constant,
the price of the bond at the beginning of each year will be $100. The sum of $1, 000 will buy 10 bonds at the beginning of year one. At the end of the year the coupons will pay 10 × 8 = 80 dollars, enough to buy 0.8 bonds at $100 each. As a result, the investor will be holding 10 + 0.8 = 10.8 bonds in year two. At the end of that year the coupons will pay 10.8 ×8 = 86.4 dollars and 0.864 additional bonds will be purchased at $100 each. The number of bonds held in year three will be 10.8 + 0.864 = 11.664, and so on. In general, the number of bonds held in year n will be

[latex]10\left(1+\frac{8}{100} \right)^{n-1} , [/latex]

which gives 10.0000, 10.8000, 11.6640, 12.5971, 13.6049 bonds held in years one to five.

Question 2.39: The sum of $1, 000 is invested in five-year bonds with face ...

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