Which of the following investments has a larger future value: A $$100$ investment earning $10\%$ per year for $5$ years or a $$100$ investment earning $5\%$ per year for $10$ years?

An investment of $$100$ invested at $5\%$ per year for $10$ years because it has a future value of $$161\mathrm{.}05.$

An investment of $$100$ invested at $10\%$ per year for $5$ years because it has a future value of $$161\mathrm{.}05.$

An investment of $$100$ invested at $10\%$ per year for $5$ years because it has a future value of $$162\mathrm{.}89.$

An investment of $$100$ invested at $5\%$ per year for $10$ years because it has a future value of $$162\mathrm{.}89.$

The values are equal