Question

Time to reach a financial goal You have $42,180.53 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 12 percent annually on the account. How many years will it take to reach your goal?

Answer 1

Answer:

It take to reach your goal is 11 years

Explanation:

given data

initial fixed amount = $42,180.53

deposit additional = $5,000

account totals = $250,000

expect to earn r = 12%

solution

we will apply Future value of annuity that is express as

Future value of annuity = initial fixed amount ×  $(1+r)^{t}$ + deposit additional  × $\frac{(1+r)^t-1}{r}$     ......................a

put here value and we get

$250,000 = 42,180.53 \times (1+0.12)^{t} + 5,000 \times \frac{(1+0.12)^t-1}{0.12}$          

solve it we get

time t = 11

so it take to reach your goal is 11 years