From simple to gross and multi-period returns

The simple return \(R\) expresses the percentage change in the value of an investment. The corresponding so-called "gross" return is defined as the future value of 1 USD invested in the asset for one period and is thus equal to \(1+R\).

The gross return over two periods is obtained similarly. Let $R1$ be the return in the first period and $R2$ the return in the second period. Then the end-value of a 1 USD investment is \((1 +\)$R1$\() * (1 + \)$R2$\()\).

The corresponding simple return over those two periods is: \((1 +\)$R1$\() * (1 + \)$R2$\()-1\).

Suppose that you have an investment horizon of two periods. In the first period, you make a 10% return. But in the second period, you take a loss of 5%.

Use the R console to compute the end value of a 1000 USD investment.

Which of the three following answers do you obtain?