Duration of Zero Coupon Bond = 5 years
Duration of Perpetuity = 1.02/0.02 = 51 years
a.
19 = 5w + (1 - w)51
19 = 5w + 51 - 51w
w = 0.695652
Amount in Zero Coupon Bond = $695,652
Amount in Perpetuity = 1,000,000 - 695,652 = $304,348
b.
Next Year,
18 = 4w + (1 - w)51
w = 0.702128
Amount in Zero Coupon Bond = $702,128
Amount in Perpetuity = 1,000,000 - 702,128 = $$297,872
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