Rafael has decided to retire once he has $1,000,000 in his retirement account. At the end of each year, he will contribute $7,000 to the account, which is expected to provide an annual return of 6.2%. How many years will it take until he can retire

38 years

Explanation:

in order to determine the amount of years that it will take Rafael to retire, we can use the future value annuity formula:

future value = payment x annuity factor

we know:

future value = $1,000,000 payment = $7,000

annuity factor = $1,000,000 / $7,000 = 142.8571

the formula to calculate an annuity factor = [ (1 + r) ⁿ - 1] / r

142.8571 = [ (1 + 0.062) ⁿ - 1] / 0.062

8.8571 = (1.062) ⁿ - 1

9.8571 = (1.062) ⁿ

using a scientific calculator, we can determine the value of n = 38.0389491 years ≈ 38 years