Question

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.

Answer 1

Solution :

Given :

The bonds offer a $\text{real interest rate}$ of 4.5% per year

Tax rate = 10% = 0.10

Inflation rate = 2

$\text{Nominal interest rate}$ = $\text{real interest rate}$ + $\text{inflation rate}$

$\text{Nominal interest rate}$ = 2 + 4.5

                                   = 6.5

$\text{After tax nominal rate}$ = $\text{Nominal interest rate}$ $\times (1-\text{tax rate})$

$\text{After tax nominal interest rate}$ = $6.5 \times (1-0.10)$

                                                  $=6.5 \times 0.90$

                                                 = 5.85

After tax real interest rate = $\text{after tax nominal rate}$ - $\text{inflation rate}$

                                           = 5.85 - 2.0

                                            = 3.85

$\text{Inflation rate}$ = 7.0

$\text{Real interest rate = 4.5}$

$\text{Nominal interest rate}$ = $\text{real interest rate}$ + $\text{inflation rate}$

                                   = 7 + 4.5

                                  = 11.5

$\text{After tax nominal interest rate}$ = $\text{Nominal interest rate}$ $\times (1-\text{tax rate })$

                                                  $=11.5 \times (1 - 0.10)$

                                                  $=11.5 \times 0.90$

                                                = 10.35

$\text{After tax nominal interest rate}$ = 11.5 x (1 - 0.10)

                                          = 11.5 x 0.90

                                         = 10.35

$\text{After tax nominal interest rate}$ = $\text{after tax nominal rate}$ - $\text{inflation rate}$

                                           = 10.35 - 7.0

                                          = 3.35

Putting all the value in table :

$\text{Inflation rate}$    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 $\text{higher inflation rate}$, a $\text{lower inflation rate}$ 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.