Suppose you want to have $700,000 for retirement in 35 years. Your account earns 8% interest. How much would you need to deposit in the account each month?

To determine how much you need to deposit each month to reach $700,000 in 35 years with an account that earns 8% interest, we use the formula for the future value of an ordinary annuity. The formula is:

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

Where:
- $ FV $ is the future value (what you want in the future: $700,000),
- $ P $ is the monthly payment (the amount to be deposited),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (number of years multiplied by 12).

### Step 1: Identify the variables
- $ FV = 700,000 $
- Annual interest rate is 8%, so the monthly interest rate $ r = \frac{8\%}{12} = \frac{0.08}{12} = 0.00667 $
- $ n = 35 \times 12 = 420 $ (35 years and 12 months per year)

### Step 2: Rearrange the formula to solve for $ P $
We can rearrange the formula to solve for $ P $:

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

### Step 3: Plug in the values
\[
P = \frac{700,000}{\frac{(1 + 0.00667)^{420} - 1}{0.00667}}
\]

Now, I'll calculate this for you.The monthly deposit required to accumulate $700,000 in 35 years with an 8% interest rate is approximately **$305.16**.

Would you like more details on the calculation or have any questions?

Here are some related questions for further exploration:
1. How would the required monthly deposit change if the interest rate were 6%?
2. What if you wanted to accumulate $1,000,000 instead of $700,000 in the same period?
3. How much interest would be earned over the 35 years compared to your total contributions?
4. How would increasing the deposit frequency (e.g., bi-weekly instead of monthly) affect the total amount needed?
5. What if you started with an initial deposit? How would that change the required monthly payment?

**Tip:** The earlier you start saving, even small amounts, the more benefit you get from compound interest!

Find out how much you need to deposit each month to reach $700,000 for retirement in 35 years with an 8% interest rate. This detailed solution covers the future value of an ordinary annuity formula and provides a step-by-step breakdown of the calculation.

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