Question

You will receive $100 from a zero-coupon savings bond in 4 years. The nominal interest rate is 7.00%.

a. What is the present value of the proceeds from the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. If the inflation rate over the next few years is expected to be 2.00%, what will the real value of the $100 payoff be in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. What is the real interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

d. Show that the real payoff from the bond [from part (b)] discounted at the real interest rate [from part (c)] gives the same present value for the bond as you found in part (a). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solution a) Present value of proceeds from zero coupon bond = FV/(1 + r)^n

FV = Face value of bond = $100

r = discount rate = 7%

n = number of years to maturity = 4

Present value of zero coupon bond = 100/(1 +7%)^4

= 100/1.31079601

= 76.2895212

= $76.29

Solution b) Real interest rate = 2%

Real value of the $100 payoff = 100/(1 + 2%)^4

= 100/1.08243216

= 92.3845426027

= $92.38

Solution c) Real interest rate = (1 + Nominal interest rate)/(1 + inflation rate) - 1

= (1 + 7%)/(1 + 2%) - 1

= 4.9019607%

= 4.90%

Soution d) The real payoff from the bond = FV/(1 + r)^n

r = Real interest rate = 4.9019607%

n = number of years = 4

FV = Face value in real terms = 92.3845426027

Real payoff = 92.3845426027/(1 + 4.9019607%)^4

= 92.3845426027/1.2109728944

= 76.28952145

= $76.29

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answered by: anonymous