Eric 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. The government taxes nominal interest income at a rate of 10%. The following table shows two scenarios: A low-inflation scenario and a high- inflation scenario. Given the real interest rate of 4.5% per year, find the nominal interest rate on Eric's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario. Inflation Rate Real Interest Nominal Interest After-Tax After-Tax (Percent) Rate Rate Nominal Interest Rate Real Interest (Percent) (Percent) (Percent) (Percent)2.0 4.5 7.0 4.5Compared with higher inflation rates, a lower inflation rate will nominal interest income. This tends to the after-tax real interest rate when the government taxes saving, thereby the quantity of investment in the economy and the economy's long-run growth rate.

Solution :

Given :

The bonds offer a of 4.5% per year

Tax rate = 10% = 0.10

Inflation rate = 2

= +

= 2 + 4.5

                                   = 6.5

=

=

                                                 = 5.85

After tax real interest rate = -

                                           = 5.85 - 2.0

                                            = 3.85

= 7.0

= +

                                   = 7 + 4.5

                                  = 11.5

=

                                                = 10.35

= 11.5 x (1 - 0.10)

                                          = 11.5 x 0.90

                                         = 10.35

= -

                                           = 10.35 - 7.0

                                          = 3.35

Putting all the value in table :

   Real interest  Nominal interest  After tax nominal  After tax  

                                  rate                rate               interest rate       interest rate

2.0                             4.5                  6.5                        5.85                   3.85

7.0                              4.5                11.5                         10.35                3.35

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

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