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Question 2.38: Suppose that one dollar is invested in zero-coupon bonds mat...

Suppose that one dollar is invested in zero-coupon bonds maturing after one year. At the end of each year the proceeds are reinvested in new bonds of the same kind. How many bonds will be purchased at the end of year 9? Express the answer in terms of the implied continuous compounding rate.

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At time 0 we buy  1/B(0,1)=er1/B(0, 1) = e^{r } bonds, at time 1 we increase our holdings to er/B(1,2)=e2re^{r}/B(1, 2) = e^{2r} bonds, and generally at time n we purchase e(n+1)re^{(n+1)r} one-year bonds.

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