Arbitrage Possible?

Jorgen Welsher, CFA obtains the following quotes for zero coupon government bonds all with a par value of $100.

Type of Price Delivery (years) Maturity (years) Price
Spot 0 3 $91.51
Forward 2 3 $94.55
Spot 0 2 $92.45

Welsher can earn arbitrage profits by:

A)

buying the 2-year bond in the spot market, going long the forward contract and selling the 3-year bond in the spot market.

Achieved

B)

selling the 2-year bond in the spot market, going short the forward contract and buying the 3-year bond in the spot market.

Failed

C)

buying the 2-year bond in the spot market, going short the forward contract and selling the 3-year bond in the spot market.

I got the correct answer but maybe it was coincidence? This is how I solved it.

If you buy/go long you get the appreciation from the purchase price up to par so:
Spot 2 year: ($100 - $92.45) = $7.55
Forward 3 year: ($100 - $94.55) = $5.45
Short Spot 3 year (you owe the difference: ($100 - $91.51) = $8.49

$7.55 + $5.45 - *$8.49 = $4.51 in arbitrage profit?

A 3 year zero coupon is equivalent to a 2 year spot followed by reinvesting in the forward. The 3 year spot is selling for 91.51; the 2 year + forward combo has a market price of 87.411 (100 * 0.9455 * 0.9245). So the 3 year zero is overvalued.