Question

How many months do you need to work to have enough money to retire? Assume you want $1,000,000 to retire, you currently do not have any savings, but starting next month, you will be able to make monthly deposits of $500 into your retirement account that returns on average 5.5% per year compounded monthly.

Question 18 options:

	507 months
	88 months
	1056 months
	782 months

Answer 1

FV of Annuity = Monthly Payment * [{(1 + r)ⁿ - 1} / r]

$1,000,000 = $500 * [{(1 + 0.055)ⁿ - 1} / 0.055]

$1,000,000 / $500 = [{(1.055)ⁿ - 1} / 0.055]

2,000 * 0.055 = (1.055)ⁿ - 1

110 + 1 = (1.055)ⁿ

log(111) = n[log(1.055)]

4.7095 = n[0.054]

n = 4.7095 / 0.054

n = 87.96, or 88 months

So, 2nd option is correct.