Question

You will receive $100 from a zero-coupon savings bond in 4 years. The nominal interest rate is 8.20%. 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 3.20%, 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

1.
=Future value/(1+nominal rate)^t
=100/1.082^4=72.9610300948452

2.
=Future Value/(1+inflation rate)^t
=100/1.032^4=88.1619547356941

3.
=(1+nominal rate)/(1+inflatio rate)-1
=1.082/1.032-1=0.0484496124031009

4.
=Real value/(1+real rate)^4
=100/1.032^4*1/(1+1.082/1.032-1)^4=72.9610300948452