# How Long Will It Take to Save One Million Dollars?

The length of time it takes to save $1,000,000 in a savings account or other investment account depends on several factors: the amount of the initial deposit, the amount of your recurring monthly deposits (if any), and the rate of return.

Additionally, when you take into the accounts of inflation, by the time you have saved one million dollars your future money will worth much less than $1,000,000 in today's dollars.

You can use the calculator on the left to see how many years it will take to have saved one million dollars given a fixed initial deposit, fixed monthly deposits, and a set interest rate. With a given rate of annual inflation, you can also see how long you will need to save money in order to acquire an amount that is equivalent to $1,000,000 by today's standards.

See also the savings account calculator, savings goal calculator, and retirement savings calculator for similar tools.

### Example

Max makes an initial deposit of $1,500 in a savings account that has an annual interest rate of 4.05%. Each month after he deposites $750 in the account and never makes a withdrawal. Let the variables P, M, and R represent the initial depoist, monthly deposit, and*monthly decimal*interest rate respectively. Then the number of months (N) it takes to reach $1,000,000 is given by the equation

N = [ln(1000000R + M + MR) - ln(PR + M + MR)]/ln(1 + R)

where ln(x) is the natural logarithm function. In this example, P = 1500, M = 7500, and R = 0.0405/12 = 0.003375. Then N can be computed by evaluating

N = [ln(3375 + 750 + 2.53125) - ln(5.0625 + 750 + 2.53125)]/ln(1.003375)

= 503 months, or about 42 years

Now consider the effects of an annual inflation rate of 1.5% per year. In 42 years, Max's one million dollars will only be worth the equivalent of

$1000000/1.015

^{42}= $535089

by today's standards. If Max sticks to this savings scheme for 62 years (744 months), he will have $2,511,751 at the end of the 62 years. And assuming a constant inflation rate of 1.5% per year, his money will be worth

$2511751/1.015

^{62}= $997888

by today's standards, which is much closer to the one million dollar goal.

© *Had2Know 2010
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