Time to reach a financial goal You have $22,566.87 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $280,000. You expect to earn 11% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations. years

    We authentication the formula:
    A=P(1+r/100)^n
    where
    A=advenient appreciate
    P=present appreciate
    r=scold of interest
    n=season era.

    Hence advenient appreciate of $22,566.87=$22,566.87*(1.11)^n

    Also:

    Advenient appreciate of annuity=Annuity[(1+rate)^season era-1]/rate

    =$5000[(1.11)^n-1]/0.11

    Hence

    280,000=22,566.87*(1.11)^n+$5000[(1.11)^n-1]/0.11

    280,000=22,566.87*(1.11)^n+$45,454.55[(1.11)^n-1]

    280,000=22,566.87*(1.11)^n+$45,454.55*(1.11)^n-45,454.55

    (280,000+45,454.55)=(1.11)^n[22566.87+45,454.55]

    (1.11)^n=(280,000+45,454.55)/[22566.87+45,454.55]

    (1.11)^n=4.784589431

    Taking log on twain sides;

    n*log 1.11=log 4.784589431

    n=log 4.784589431/log 1.11

    =15 years(Approx).