Tom wants to retire with $1,000,000 in 30 years. If his investments earn 6% annually, how much should he approximately invest each year to reach his goal?

A. $10,000
B. $12,000
C. $15,000
D. $32,000

1 answer

To find out how much Tom should invest each year to reach his goal of $1,000,000 in 30 years with an annual interest rate of 6%, we can use the future value of an annuity formula:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Where:

  • \(FV\) is the future value of the annuity (the amount he wants, $1,000,000),
  • \(P\) is the annual payment (amount he needs to invest each year),
  • \(r\) is the annual interest rate (6% or 0.06), and
  • \(n\) is the number of years (30).

We need to rearrange this formula to solve for \(P\):

\[ P = \frac{FV \times r}{(1 + r)^n - 1} \]

Substituting the values into the formula:

  • \(FV = 1,000,000\)
  • \(r = 0.06\)
  • \(n = 30\)

Now we calculate:

\[ P = \frac{1,000,000 \times 0.06}{(1 + 0.06)^{30} - 1} \]

Calculating \((1 + 0.06)^{30}\):

\[ (1.06)^{30} \approx 5.74349 \]

Now substituting that back into the equation:

\[ P = \frac{1,000,000 \times 0.06}{5.74349 - 1} \]

Calculating the denominator:

\[ 5.74349 - 1 \approx 4.74349 \]

Now substitute this value back into the equation for \(P\):

\[ P \approx \frac{60,000}{4.74349} \approx 12,629.70 \]

Thus, Tom should invest approximately $12,630 each year. The closest answer from the options given is:

B. $12,000 (as it's the closest approximation).