Question

Suppose the real interest rate is 2.8%, and the inflation rate is 7%. (1) How much do you need to invest now in order to get $100 in a year? Please show two approaches to calculate the answers. (Round your final answer to two decimal places) (2) Suppose the U.S. Treasury issues 5% coupon, 3-year TIPS (Treasury Inflation-Protected Securities). What are the real cash flows on the 3-year TIPS each year? What are the nominal cash flows on the 3-years TIPS each year? (Round your final answers to two decimal places)

Answer 1

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