Question

If there is a 20 year, 10% rate of return with 0 initial investment, $100 annual investment, expected inflation rate of 5%, how much money will I lose when accounting for inflation?

A. Less than $1000

B. Between $1000 and $2000

C. Between $2000 and $3000

D. More than $3000

Answer 1

Answer: Option D: More than $3000

given

Annual Payment A=$500

r=10%

n=20 years

if there is no inflation then FV of annuity

FV=A*((1+r)^n-1)/r=500*((1+10%)^20-1)/10%

FV=$28637.50 Eq 1

if there is inflation of 5% then real rate of return r=10%-5%=5%

then FV of annuity

FV=A*((1+r)^n-1)/r=500*((1+5%)^20-1)/5%

FV=$16532.98 Eq 2

From equation 1 and 2 we found that

Money I will lose for accounting inflation= 28637.50 - 16532.98=$12104.52