Suppose that the nominal interest rate is $10$ percent compounded monthly. We want to compare $$125,000$ received today to $$200,000$ received in $5$ years.

$($a$)(3$ pts$.)$ What is the future value of the amount received today $($$$)?$ Round you answer to the nearest dollar.

Answer $1$ Question $7$

$($b$)(2$ pts$.)$ What is the nominal interest rate $($percent$)$ needed so the amount received today would increase to the amount being offered in the future $($compounded monthly$)?$ Express your answer as a percent $($i$.$e$.,5\mathrm{.}00\%$ would be entered as $5\mathrm{.}00)$ and be accurate to two decimal places.