Numerical problem IV $(12$p$)$

$($a$)$ A stock price index increases from $100$ to $33,000$ over the course of $100$ years. What

is the geometric average rate of return?

$($b$)$ Over the same time period, the consumer price index increases from $3,000$ to $45,000.$

What is the geometric average inflation rate?

$($c$)$ What is the geometric average real rate of return on the stock price index?

$($d$)$ If the dividend yield is $4\%$ per year, what is the total rate of return on the stock

price index before inflation?