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.