Question

#7 Your aunt has given you a savings bond. This savings bond will give you $100 in 3 years. This bond has a nominal interest rate of 8%. Determine the following:

1. What is the present value of this bond?
2. Inflation is projected to be 3% for the next 5 years. What is the real value of that $100 face value, in today’s dollars?
3. Compute the real interest rate of the bond.
4. What is the difference in PV from part A, the nominal payout, vs. the real payout in part B when discounted with the real interest rate found in part C?

Answer 1

Savings bond Value = $100

Years = 3

Nominal interest rate = 8%

1. Present value of this bond:

Present Value = Savings Bond Value in Year 3 * Discount factor at nominal interest rate for 3rd year

=$100 * (1/(1+8%)^3) = $100*0.7938 = $79.38

Present Value of Bond = $79.38

2. Real value of that $100 face value, in today’s dollars:

Inflation = 3%

Real Value = Savings Bond Value in Year 3 * Discount factor at inflation rate for 3rd year

=$100 * (1/(1+3%)^3) = $100*0.9151 = $91.51

Real value of that $100 face value, in today’s dollars = $91.51

3. Real interest rate of the bond:

Real Interest rate = ((1+Nominal interest rate) / (1+Inflation rate)) - 1 =

= ((1+8%)/(1+3%))-1 = 1.04854-1 = 0.04854 or 4.854%

Real interest rate of the bond = 4.854%

4. Difference between PV from part A, the nominal payout, vs. the real payout in part B when discounted with the real interest rate found in part C:

Present Value of Bond as per part A above, Nominal Payout = $79.38

Real Payout in part B when discounted with the real interest rate found in part C = Real Value of the bond * Discount factor at real interest rate for 3rd year = $91.51*(1/(1+4.854%)^3) = $91.51*0.8675 = $79.38

Thus, Real Payout = Nominal Payout = $79.38

Hence, there is no difference between PV from part A, the nominal payout, vs. the real payout in part B when discounted with the real interest rate found in part C.