Question

Jake receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 4.5% per year. The nominal interest rate on the bonds adjusts automatically to account for the inflation rate.


Given the real interest rate of 4.5% per year, find the nominal interest rate on Sean's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario.


Inflation Rate Real Interest Rate Nominal Interest Rate After-Tax After-Tax

Nominal Interest Rate Real Interest Rate


(Percent) (Percent) (Percent) (Percent) (Percent)


2.0 4.5

8.5 4.5


Compared with lower inflation rates, a higher inflation rate will the after-tax real interest rate when the government taxes nominal interest income. This tends to saving, thereby the quantity of investment in the economy and the economy's long-run growth rate.

Answer 1

Answer:

First we find the nominal interest rate under the two scenarios. The formula is:

Nominal Interest Rate = Inflation Rate + Real Interest Rate

Nominal Interest Rate first scenario = 2.0 + 4.5

                                                           = 6.5

Nominal interest rate second scenario = 8.5 + 4.5

                                                                = 13

Now we find the after-tax nominal interest rate. The formula is:

After tax nominal interest rate = nominal interest rate x (1 - tax rate)

We will assume that the tax rate is 10%.

After tax nominal interest rate first scenario = 6.5 x (1 - 0.1)

                                                                         = 5.85

After tax nominal interest rate second scenario = 13 x (1 - 0.1)

                                                                               = 11.7

Finally, we find the after-tax real interst rate. The formula is:

The formula is the same as above, the only difference is that the real interest rates are used instead.

After tax real interest rate first scenario = 4.5 x (1 - 0.1)

                                                                  = 4.05

After tax real interest rate second scenario = 4.5 x (1 - 0.1)

                                                                        = 4.05