Question

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

Answer 1

Answer:

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.