Following are current prices for pure discount bonds with face value of $1,250 of different maturities as of 1 January 2022. Calculate the spot interest rates for each bond.

Bond Maturity	Price	Bond Maturity	Price
1 year	$1,190.48	3 years	$1,049.52
2 years	$1,123.07	4 years	$ 953.62

Assume the expectations theory is valid. Based on your results in part (a), determine the spot 1-year, 2-year, and 3-year rates expected 1 year later on 1 January 2023.