Question

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?

Answer 1

it take to reach your goal is 14 years

Step-by-step 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 ×
`(1+r)^(t)` + deposit additional ×
`((1+r)^t-1)/(r)` .................1

put here value and we get

$240,000 = $11,849.93 ×
`(1+0.13)^(t)` + $5,000 ×
`((1+0.13)^t-1)/(0.13)`

solve it we get

time t = 14

so it take to reach your goal is 14 years