Question

You have $42,180.53 in your bank account, and plan to add 5,000 at the end of each future years until it reaches $250,000. You expect to earn 10% annually on the account, how many years will it takes to reach your goal?

Answer 1

We can find out the no.of years required to reach a goal of $250000 by using future value of sum and future value of annuity formula.

Let us assume the 'n' be the no.of years required.

Future value of sum = $42180.53*(1+0.10)^n

Future value of annuity = $5000*{[(1+0.10)^n -1]/0.10}

Hence we will write the equation as

$250000 = [$42180.53*(1+0.10)^n] + [$5000*{[(1+0.10)^n -1]/0.10}]

$250000 = [$42180.53*1.10^n] + [$5000*{(1.10^n -1]/0.10}]

n = 12.38 years

No.of years required to reach your goal = 12.38 years