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Sagot :
Solution :
Given :
The bonds offer a [tex]\text{real interest rate}[/tex] of 4.5% per year
Tax rate = 10% = 0.10
Inflation rate = 2
[tex]\text{Nominal interest rate}[/tex] = [tex]\text{real interest rate}[/tex] + [tex]\text{inflation rate}[/tex]
[tex]\text{Nominal interest rate}[/tex] = 2 + 4.5
= 6.5
[tex]\text{After tax nominal rate}[/tex] = [tex]\text{Nominal interest rate}[/tex] [tex]$\times (1-\text{tax rate})$[/tex]
[tex]\text{After tax nominal interest rate}[/tex] = [tex]$6.5 \times (1-0.10)$[/tex]
[tex]$=6.5 \times 0.90$[/tex]
= 5.85
After tax real interest rate = [tex]\text{after tax nominal rate}[/tex] - [tex]\text{inflation rate}[/tex]
= 5.85 - 2.0
= 3.85
[tex]\text{Inflation rate}[/tex] = 7.0
[tex]\text{Real interest rate = 4.5}[/tex]
[tex]\text{Nominal interest rate}[/tex] = [tex]\text{real interest rate}[/tex] + [tex]\text{inflation rate}[/tex]
= 7 + 4.5
= 11.5
[tex]\text{After tax nominal interest rate}[/tex] = [tex]\text{Nominal interest rate}[/tex] [tex]$\times (1-\text{tax rate })$[/tex]
[tex]$=11.5 \times (1 - 0.10)$[/tex]
[tex]$=11.5 \times 0.90$[/tex]
= 10.35
[tex]\text{After tax nominal interest rate}[/tex] = 11.5 x (1 - 0.10)
= 11.5 x 0.90
= 10.35
[tex]\text{After tax nominal interest rate}[/tex] = [tex]\text{after tax nominal rate}[/tex] - [tex]\text{inflation rate}[/tex]
�� = 10.35 - 7.0
= 3.35
Putting all the value in table :
[tex]\text{Inflation rate}[/tex] 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 [tex]\text{higher inflation rate}[/tex], a [tex]\text{lower inflation rate}[/tex] 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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