Question

Time to reach a financial goal You have $44,976.27 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $220,000. 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.

Answer 1

Amount in account now	44976.27
Financial goal	220000
Amount remaining	220000 - 44976.27
Amount remaining	175023.73
The amount remaining is the future value of the annuity.
Future value of the annuity = 175023.73
Future value of an annuity = C*[((1+r)^t-1)/r]
where C is the annuity payment that is 4000.
r is the interest rate that is 11%.
t is the time period in years
175023.73 = 4000*[((1.11)^t-1)/.11]
4000*((1.11)^t-1) = 175023.73*.11
4000*((1.11)^t-1) = 19252.61
((1.11)^t - 1) = 4.813153
(1.11)^t = 5.813153
tln(1.11) = ln(5.813153)
t*(.10436) = 1.76012
t = 1.76012/.10436
t = 16.86585
It will take 16.87 years for you to reach your goal.