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You have $11,849.93 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $240,000. You expect to earn 13% annually on the account. How many years will it take to reach your goal?

Respuesta :

Answer:

it take to reach your goal is 14 years

Explanation:

given data

initial fixed amount = $11,849.93

deposit additional = $5,000

account totals = $240,000

expect to earn r = 13%

solution

we apply here Future value of annuity that is

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

put here value and we get

$240,000 = $11,849.93  × [tex](1+0.13)^{t}[/tex] + $5,000 ×  [tex]\frac{(1+0.13)^t-1}{0.13}[/tex]    

solve it we get

time t = 14

so it take to reach your goal is 14 years