Question

5.

TIME TO REACH A FINANCIAL GOAL

You have $56,899.31 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $270,000. You expect to earn 10% 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

Answer 1

Amount in the brokerage account = P = $56,899.31

P1 = Annual Deposit = $3,000

r = interest rate = 10%

n = number of years

Amount required = [P * (1+r)^n] + [P1 * [(1+r)^n - 1] / r]

$270,000 = [$56,899.31 * (1+10%)^n] + [$3,000 * [(1+10%)^n - 1] / 10%]

$270,000 = [$56,899.31 *(1.1)^n] + [$30,000 * [(1.1)^n - 1]]

$240,000 = $86,899.31 * (1.1)^n

(1.1)^n = 2.7618171

n = log(2.7618171) / log(1.1)

n = 0.441194914 / 0.0413926852

n = 10.6587652 years

Therefore, it wil take 10.66 years to reach the goal