Question

Consider the following three zero-coupon (discount) bonds:

Bond	Face Value	Time to Maturity	Market Price
1	$1,000	One year	$924.64
2	$1,000	Two years	$841.53
3	$1,000	Three years	$744.59

a) Calculate the one-, two-, and three-year spot rates.

b) Calculate the forward rate over the second year and the forward rate over the third year.

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

B E F G H Bond Forward Rate C D Zero-Coupon Bond Face Value | Time to Maturity $1,000 One year $1,000 Two years $1,000 Three years Market Price $924.64 $841.53 $744.59 Spot Rate 8.15% 9.01% 10.33% 9.88% 13.02%

Cell reference -

- A B C D E Zero-Coupon Bond Bond Face Value Time to Maturity Market Price 1 1000 One year 924.64 1000 Two years 841.53 1000 Three years 744.59 Spot Rate Forward Rate =(C3/E3)^(1/B3)-1 =(C4/E4)^(1/B4)-1 =((1+F4)^B4)/(1+F3)-1 =(C5/E5)^(1/85)-1 =((1+F5)^B5)/(1+F4)^B4-1

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.