Against expert advice, you begin your retirement savings at age 40. You plan to retire at  age 65. How much will you need to deposit each month into a savings account with an  annual interest rate of 6% compounded monthly if your goal is to save $150,000? 

To calculate how much you need to deposit each month into a savings account with an annual interest rate of 6% compounded monthly, we can use the **future value of an ordinary annuity formula**, since you will make regular monthly deposits.

The formula is:

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

Where:
- $ FV $ is the future value, which is $150,000.
- $ P $ is the monthly deposit (what we are solving for).
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12. In this case, $ r = \frac{6\%}{12} = 0.005 $.
- $ n $ is the total number of months (the number of years times 12). In this case, $ n = (65 - 40) \times 12 = 25 \times 12 = 300 $.

Now we can rearrange the formula to solve for $ P $:

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

Let’s plug in the values and compute it.To achieve your goal of saving $150,000 by the time you retire at age 65, you will need to deposit approximately **$216.45** each month into the savings account with a 6% annual interest rate, compounded monthly.

Do you want more details or have any questions?

Here are 5 related questions to consider:
1. How does the interest rate affect the amount you need to save monthly?
2. What if you started saving earlier, say at age 30 instead of 40?
3. How would the savings goal change if the interest rate were lower, say 4%?
4. How does compounding frequency (e.g., monthly vs. quarterly) influence the final amount?
5. What happens if you want to save a larger amount, say $200,000?

**Tip:** Starting to save earlier significantly reduces the amount you need to deposit monthly, as compound interest has more time to work.

Against expert advice, you begin your retirement savings at age 40. You plan to retire at age 65. How much will you need to deposit each month into a savings account with an annual interest rate of 6% compounded monthly if your goal is to save $150,000?

Find out how much you need to deposit each month to reach your retirement goal of $150,000 by age 65, starting at age 40, with an annual interest rate of 6% compounded monthly. Learn the key formulas and concepts behind compound interest and ordinary annuities.

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