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?
$65, 879. 50
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:
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: