# Over the course of 10 years, someone puts $400 per month into an investment account that earns 6% per year (compounds monthly). What is the value of the account at the end of 10 years?

##### 1 Answer

$65, 879. 50

#### Explanation:

Let's work this out month by month for a few months, find the pattern, then solve.

We're putting $400 per month into an account that is earning 6% per year with the interest compounding monthly.

Let's work out the interest rate first: we have

We start month 1 by adding $400 to our account. We earn interest over the month, so have

In month 2, we add $400 to the account,

Is there a pattern yet?

Let's do one more and I think it will be clear:

In month 3, we add $400 to the account,

Let's look at how we got here:

This is

and far easier to compute on a spreadsheet or a financial calculator.

The answer I came up with on my spreadsheet is $65, 879. 50. I also worked it out on an online financial calculator and it returned $65, 551. 74 - which is what my sheet returned at the start of Month 120 but I calculated it through with that last month's interest (and so I think my answer is correct).

Here is where that financial calculator that I mentioned is located:

http://www.financialcalculator.org/investing/interest-calculator