Question

You have $36,899.31 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. You expect to earn 10% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.

Answer 1

To reach a goal of $250,000 in a brokerage account with an annual deposit of $5,000 and an annual interest rate of 10%, it will take approximately 18.2 years.

Step-by-step explanation:

To determine how many years it will take to reach your goal of $250,000 in the brokerage account, you need to use the formula for calculating the future value of an annuity. The formula is V = P * [(1 + r)^n - 1] / r, where V is the desired future value, P is the annual deposit, r is the annual interest rate, and n is the number of years. In this case, V = $250,000, P = $5,000, and r = 10% (0.1). Plug in these values and solve for n: 250,000 = 5,000 * [(1 + 0.1)^n - 1] / 0.1 After simplifying the equation, the result is n = log(250,000 / 5,000 * 0.1 + 1) / log(1 + 0.1). Using a scientific calculator or software, you can calculate that n is approximately 18.2 years.