Question

Your rich uncle gave you $10,000 today on your 20th birthday. You want to invest the money and then start making monthly deposits, beginning one month from today, so that you will accumulate $500,000 by the time you are 60 years old. You believe that you can earn 8% on your investment. How much will you have to deposit each month to reach your goal of $500,000 by your 60th birthday?

$126 - $150

More than $150

$76 - $100

Less than $75

$101 - $125

Answer 1

Answer is “Less than $75”

Initial Deposit = $10,000
Desired Sum = $500,000
Time Period = 40 years or 480 months

Annual Interest Rate = 8.00%
Monthly Interest Rate = 0.6667%

Let monthly deposit be $x

$10,000*1.006667^480 + $x*1.006667^479 + $x*1.006667^478 + …. + $x*1.006667 + $x = $500,000
$10,000 * 1.006667^480 + $x * (1.006667^480 - 1) / 0.006667 = $500,000
$10,000 * 24.273386 + $x * 3,491.007831 = $500,000
$242,733.86 + $x * 3,491.007831 = $500,000
$x * 3,491.007831 = $257,266.14
$x = $73.69

Monthly Deposit = $73.69