Question

Peter Goodman invested $40,000 in the Carters balanced mutual fund 5 years ago and he is looking for advice on whether to sell this investment. He is really concerned about his return being influenced by inflation. His tax rate is 30% and the inflation rate is 1.5% p.a. Assume that taxes will be paid when he sells the investment. His investment accounts earned the following annual rates of return: +2%, +8%, +5%, +1%, -4%. a) Calculate the arithmetic and geometric mean rate of return on his investments before tax. b) As his financial advisor, what mean (geometric vs. arithmetic) would you present to him and why? c) Calculate Peter’s real after-tax rate of return

Answer 1

Answer A) I have Calculated Arthmetic Mean by using excel using AVERAGE formula

	Returns %
	2
	8
	5
	1
	-4
Arithemetic Mean	2.40 %

I have calculated Geometrix mean by using excel by using this formula :

​[(1+R1​)×(1+R2​)×(1+R3​)…×(1+Rn​)]n1​−1where:R=Returnn=Count of the numbers in the series​

Returns
0.02	1.02
0.08	1.08
0.05	1.05
0.01	1.01
-0.04	0.96
Geometric Mean	2.32

Answer B) The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean.