So you can retire early, you have decided to start saving $500 a month starting one month from now. you plan to retire as soon as you can accumulate $1 million. if you can earn 5 percent on your savings, how many years will it be before you can retire?
a) 33.39 years
b) 42.87 years
c) 44.76 years
d) 44.71 years
e) 33.87 years

D) 44.76 years

Explanation:

To find the retirement year, we need to use annuity formula for the future value of Time Value of Money as I am planning to get $1,000,000.

FV = PMT x [{(1 + r)^n} - 1]/r

Here,

FV = Future Value = $1,000,000

PMT = $500

r = 5%/12 = 0.05/12 = 0.004167 (Since the payment is monthly, we have to divide the percentage by 12, or m=12)

Therefore, putting the value in the formula;

$1,000,000 = $500 x [{(1+0.004167)^n} - 1]/0.004167

or, $2,000 = (1.004167^n) - 1/0.004167

or, 8.334 = (1.004167^n) - 1

or, 9.334 = 1.004167^n

or, log 9.334 = n log 1.004167

or, 0.97007 = n x 0.001806

or, n = 537.1537 periods

Since, we will pay monthly payment, we have to divide the periods by 12 to get the exact year. Therefore,

n = 537.1537/12 = 44.76 years.