Question

Think about a country where there’s a 30% tax on investment income. For each of the following investment scenarios, work out the real interest rate (i.e. the real rate of return, what you’d earn if there were no taxes), the nominal after-tax rate of return, and the real after-tax rate of return:

(a) Nominal rate of return (i) = 6%, π = 4%

(b) Nominal rate of return (i) = 0.65%, π = 0.8%

(c) Nominal rate of return (i) = 2%, π = 2%

(d) Nominal interest rate (i) = 7%, π = 6%

Answer 1

	(a)	(b)	(c)	(d)
Nominal Rate of return	6%	0.65%	2%	7%
Inflation rate(π)	4%	0.8%	2%	6%
Real interest rate (before tax) (Nominal Rate of return - Inflation rate)	6 - 4 =2%	0.65 - 0.8 = -0.15%	2 - 2 = 0 %	7 - 6 = 1%
30% tax on nominal rate (30% of Nominal Rate of return = 0.3 × Nominal Rate of return)	0.3 × 6 = 1.8%	0.3 × 0.65 = 0.195%	0.3 × 2 = 0.6%	0.3 × 7 = 2.1%
Nominal after-tax rate of return (Nominal Rate of return - 30% tax on nominal rate)	6 - 1.8 = 4.2%	0.65 - 0.195 = 0.455%	2 - 0.6 = 1.4%	7 - 2.1 = 4.9%
Real after-tax rate of return (Nominal after-tax rate of return - Inflation Rate)	4.2 - 4 = 0.4%	0.455 - 0.8 = -0.345%	1.4 - 2 = -0.6%	4.9 - 6 = -1.1%