Question

You will receive $100 from a zero-coupon savings bond in 3 years. The nominal interest rate is 8%.

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 3%, 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

a. What is the present value of the proceeds from the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
=Payoff/(1+nominal rate)^t
=100/1.08^3
=79.3832241

b. If the inflation rate over the next few years is expected to be 3%, 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.)
=Payoff/(1+inflation rate)^t
=100/1.03^3
=91.51416594

c. What is the real interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
=(1+nominal rate)/(1+inflation rate)-1
=1.08/1.03-1
=4.854369%

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.)
=91.51416594/(1+4.854369%)^3
=79.38322395