Question

suppose you invest in two year treasury bill with a coupon of 5% and $1000 par. Suppose that you buy this bond at a price of exactly $1000. you intend to hold the bond to maturity and reinvest the coupons until the bond matures . you expect to reinvest the coupons in an account that pays an APR of 2.25% with semi annual compounding . calculate EAY effective interest rate

Answer 1

The EAY is computed as follows:

Value of coupons which are reinvested is computed as follows:

= (5% / 2 x $ 1,000) x (1 + 0.0225 / 2)³ + (5% / 2 x $ 1,000) x (1 + 0.0225 / 2)² + (5% / 2 x $ 1,000) x (1 + 0.0225 / 2)¹ + 5% / 2 x $ 1,000

= $ 25 x 1.01125³ + $ 25 x 1.01125² + $ 25 x 1.01125 + $ 25

= $ 101.7001918

So, the EAY will be:

= [ ($ 101.7001918 + $ 1,000) / $ 1,000 ] ^{1 / 2} - 1

= 4.96% Approximately

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