oth you and your older brother would like to have $$23,000$ in $15$ years. Because of your success in this class, you feel that you are a more savry

vestor than your brother and will be able to earn an annual return of $11$ percent compared to your brother's $9\mathrm{.}7$ percent. How much less than your

other will you have to deposit today? $($Assume annual compounding.$)$

You expect to receive a payout from a trust fund in $3$ years. The payout will be for $$12,600.$ You plan to invest the money at an annual rate of $5\mathrm{.}7$

percent until the account is worth $$21,400.$ How many years do you have to wait from today?