Answer to Question #246796 in Financial Math for Surendra Singh

Question

You want to have $200,000 in your account when you retire in 30 years. Your retirement account earns 8% interest. How much do you need to deposit each month to meet your retirement goal?

Answer 1

We’re looking for d.

r = 0.08, 8% annual rate

k = 12, since we’re depositing monthly

t = 30, 30 years

A = $200,000 The amount we want to have in 30 years

In this case, we’re going to have to set up the equation, and solve for d.

$200,000 = \frac{d \times ((1 + \frac{0.08}{12})^{30(12)} - 1)} { \frac {0.08}{12} } \\ 200,000 = \frac{{d\left( {{{\left( {1.00667} \right)}^{360}} - 1} \right)}}{{\left( {0.00667} \right)}}\\$

$200,000 = d \times (1491.57) \\ d = \frac {200,000}{1491.57}$

= $134.09

So, you would need to deposit $134.09 each month to have $200,000 in 30 years if your account earns 8% interest