Florence wishes to retire at age 65
 with $1,700,000
 in her retirement account. When she turns 22
, she decides to begin depositing money into an account with an APR of 7%
 compounded monthly. What is the monthly deposit that Florence must make in order to reach her goal? Round your answer to the nearest cent, if necessary.

To solve this problem, we will use the **Future Value of an Annuity formula** because Florence is making regular monthly deposits into her retirement account. The formula is:

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

Where:
- $ FV $ is the future value (the amount Florence wants in her retirement account: \$1,700,000).
- $ P $ is the monthly deposit.
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of deposits (number of months from age 22 to 65).

### Step 1: Calculate the monthly interest rate $ r $
The annual interest rate is 7%, so the monthly interest rate is:
\[
r = \frac{7\%}{12} = \frac{0.07}{12} = 0.0058333
\]

### Step 2: Calculate the total number of deposits $ n $
Florence will be making monthly deposits from age 22 to age 65. The number of years is:
\[
65 - 22 = 43 \text{ years}
\]
Since deposits are made monthly, the total number of deposits is:
\[
n = 43 \times 12 = 516 \text{ months}
\]

### Step 3: Solve for the monthly deposit $ P $
Rearranging the Future Value formula to solve for $ P $:
\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

Substituting the known values:
\[
P = \frac{1,700,000 \times 0.0058333}{(1 + 0.0058333)^{516} - 1}
\]

Now, let me calculate the value of $ P $.The monthly deposit that Florence must make to reach her goal of \$1,700,000 by the time she retires at age 65 is approximately **\$518.90**.

Would you like more details or have any questions?

Here are some related questions:
1. How would the monthly deposit change if the interest rate was 6% instead of 7%?
2. What if Florence started saving at age 30 instead of 22?
3. How much total interest will Florence earn by the time she retires?
4. What happens if Florence makes yearly deposits instead of monthly ones?
5. How would the final amount change if Florence decided to withdraw from the account periodically after retirement?

**Tip:** Starting early with even small deposits can make a significant difference due to compound interest over time.

Florence wishes to retire at age 65 with $1,700,000 in her retirement account. When she turns 22, she decides to begin depositing money into an account with an APR of 7% compounded monthly. What is the monthly deposit that Florence must make in order to reach her goal? Round your answer to the nearest cent, if necessary.

Discover how to calculate the monthly deposit required for Florence to retire with $1,700,000 by age 65, starting at age 22. This example explains how compound interest and annuities work using a 7% APR compounded monthly over 43 years, with a detailed step-by-step solution.

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