Question

You are 21 years old today. Starting one month from now, if you deposit $500 per month for 32 years into your retirement account which earns 0.7 percent per month, are you a millionaire by age of 53? part 1 - Find out how much money you will have by age of 53. If that number is greater than one million, then you are a millionaire by that age. Part 2 -Find out how many months it takes to reach one million of saving. If the length of time is less than 32 years, then you shold be a millionaire by age of 53. Should give you the same conclusion as in Part 1.

Answer 1

Part 1:

Monthly payment PMT = 500

Number of months n = 32 x 12 = 384

Monthly interest rate i = 0.7%

Future value FV = PMT x [(1 + i)ⁿ - 1] / i = 500 x [1.007³⁸⁴ -1] / 0.007 = $968,943.43

So you will not be a millionaire by age 53

Part 2:

FV = PMT x [(1 + i)ⁿ - 1] / i

1,000,000 = 500 x [ 1.007ⁿ - 1] / 0.007

1.007ⁿ - 1 = 1,000,000 x 0.007 / 500 = 14

1.007ⁿ = 15

n x ln(1.007) = ln(15)

0.00698 x n = 2.708

n = 388.216 months

388.216 / 12 = 32.35 years which is greater than 32 years, so you will not become a millionaire by age 53