Ruby wishes to retire at age 65
65
with $1,600,000
$
⁢
1,600,000
in her retirement account. When she turns 25
25
, she decides to begin depositing money into an account with an APR of 8%
8
%
compounded monthly. What is the monthly deposit that Ruby must make in order to reach her goal? Round your answer to the nearest cent, if necessary.

To calculate the monthly deposit Ruby must make, we can use the **Future Value of an Annuity formula**, since the situation involves regular monthly deposits compounded monthly.

The formula is:

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

Where:
- $FV$ is the future value (Ruby's goal), which is $1,600,000.
- $P$ is the monthly deposit we need to find.
- $r$ is the annual interest rate (8%, or 0.08).
- $n$ is the number of times the interest is compounded per year (since it's monthly compounding, $n = 12$).
- $t$ is the number of years the deposits are made (from age 25 to 65, so $t = 40$).

Rearranging the formula to solve for $P$:

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

Now, let's calculate it step by step.Ruby must make a monthly deposit of approximately **$458.32** to reach her goal of $1,600,000 by the time she retires at age 65.

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions you might explore:
1. How would the monthly deposit change if the interest rate were 6% instead of 8%?
2. What if Ruby started saving at age 30 instead of 25?
3. How much will Ruby have if she contributes $500 per month instead of $458.32?
4. What effect would quarterly compounding have instead of monthly compounding?
5. How much would Ruby need to deposit if she wanted to retire with $2,000,000?

**Tip:** Starting early with retirement savings allows you to benefit more from compound interest, reducing the amount you need to deposit regularly.

Ruby wishes to retire at age 65 with $1,600,000 in her retirement account. When she turns 25, she decides to begin depositing money into an account with an APR of 8% compounded monthly. What is the monthly deposit that Ruby must make in order to reach her goal? Round your answer to the nearest cent, if necessary.

Find out how to calculate the monthly deposit needed to reach a $1,600,000 retirement goal at 8% APR, compounded monthly. Learn key concepts like compound interest, future value of annuities, and step-by-step calculations. Ideal for college-level finance and business math students.

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