Answer:
1)
approach 1, using the approximate real and nominal interest rates:
nominal interest rate = real interest rate + inflation rate = 2.8% + 7% = 9.8%
present value = $100 / (1 + 9.8%) = $91.07
approach 2, using the exact real and nominal interest rates:
(1 + i) = (1 + r) × (1 + π)
(1 + i) = (1 + 2.8%) x (1 + 7%) = 1.09996
i = 1.09996 - 1 = 0.09996 = 9.996%
present value = $100 / (1 + 9.996%) = $90.91
2)
assuming a $1,000 TIPS, nominal cash flow year 1 = $50
new face value = $1,070
nominal cash flow year 2 = $53.50
new face value = $1,144.90
nominal cash flows year 3 = $57.25 + ($1,144.90 x 1.07) = $1,282.29
assuming a $1,000 TIPS, real cash flow year 1 = $50 / 1.07 = $46.73
new face value = $1,070
real cash flow year 2 = $53.50 / 1.07² = $46.73
new face value = $1,144.90
real cash flows year 3 = [$57.25 + ($1,144.90 x 1.07)] / 1.07³ = $1,282.29 / 1.07³ = $1,046.73
