In order to accumulate enough money for a down payment on a house, a couple deposits $572 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?

To determine how much money will be in the account after 6 years, we can use the formula for the future value of an annuity, since the couple is making regular monthly deposits into an interest-bearing account.

The future value of an annuity is given by:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the regular payment ($572).
- $r$ is the monthly interest rate (annual rate divided by 12 months).
- $n$ is the total number of payments (monthly payments multiplied by the number of years).

### Step 1: Identify the variables
- $P = 572$ (monthly payment).
- The annual interest rate is 3%, so the monthly interest rate is:
  \[
  r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
  \]
- The number of months over 6 years is:
  \[
  n = 6 \times 12 = 72
  \]

### Step 2: Plug the values into the formula

\[
FV = 572 \times \frac{(1 + 0.0025)^{72} - 1}{0.0025}
\]

Now, let's calculate this.The total amount in the account after 6 years will be approximately **$45,061.81**.

Would you like further details or have any questions about this calculation?

Here are 5 related questions for deeper understanding:
1. How would the total change if the interest rate were higher or lower?
2. What if the couple deposited more money each month?
3. How does compound interest affect the total over time?
4. What if the couple made deposits at the beginning of each month instead of the end?
5. How would the total be affected if the savings period were extended to 10 years?

**Tip:** Increasing the frequency of compounding (monthly vs. annually) results in greater interest accumulation over time.

Calculate the future value of monthly deposits into an account paying 3% interest compounded monthly over 6 years. With a regular deposit of $572 per month, the total savings at the end of the period will be $45,061.81. Understand the impact of compound interest and annuity formulas.

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