Compute the future value of $$100$ at an interest rate of $12$ percent $5,10,$ and $15$ years into the future. What would the future value be over these time horizons if the interest rate were $6$ percent?

Instructions: Enter your responses rounded to the nearest penny $($two decimal places$).$ Do not round intermediate calculations.

At an interest rate of $12$ percent:

Future value in $5$ years $=$ $ $176\mathrm{.}23$ Numeric ResponseEdit Unavailable. $176\mathrm{.}23$ correct.

Future value in $10$ years $=$ $ $310\mathrm{.}58$ Numeric ResponseEdit Unavailable. $310\mathrm{.}58$ correct.

Future value in $15$ years $=$ $ $573\mathrm{.}76$ Numeric ResponseEdit Unavailable. $573\mathrm{.}76$ incorrect.

At an interest rate of $6$ percent:

Future value in $5$ years $=$ $ $133\mathrm{.}82$ Numeric ResponseEdit Unavailable. $133\mathrm{.}82$ correct.

Future value in $10$ years $=$ $ $179\mathrm{.}08$ Numeric ResponseEdit Unavailable. $179\mathrm{.}08$ correct.

Future value in $15$ years $=$ $ $240\mathrm{.}65$ Numeric ResponseEdit Unavailable. $240\mathrm{.}65$ incorrect.

The patterns over different time horizons and at different interest rates show that as the time horizon lengthens, the future value increases Correct. As the interest rate declines, the future value decreases Correct.