Recently, More Money 4U offered an annuity that pays 6.6 % compounded monthly. If $2154 is deposited into this annuity every​ month, how much is in the account after 6 ​years? How much of this is​ interest?

To solve this problem, we need to use the future value of an ordinary annuity formula, where payments are made at regular intervals (monthly) and the interest is compounded periodically (monthly in this case).

### Step 1: Define the variables.
- **$ P $**: The monthly deposit = $2154
- **$ r $**: The monthly interest rate = $ \frac{6.6\%}{12} = \frac{0.066}{12} = 0.0055 $
- **$ t $**: The time in years = 6 years
- **$ n $**: The number of compounding periods per year = 12 (monthly compounding)
- **$ N $**: The total number of periods = $ n \times t = 12 \times 6 = 72 $

### Step 2: Use the future value of an ordinary annuity formula.
\[
FV = P \times \frac{(1 + r)^N - 1}{r}
\]

### Step 3: Plug in the values.
\[
FV = 2154 \times \frac{(1 + 0.0055)^{72} - 1}{0.0055}
\]

Let me calculate that for you.The future value of the annuity after 6 years is approximately **$189,653.04**.

### Step 4: Calculate the total amount deposited.
Since the deposit is $2154 per month for 72 months:
\[
\text{Total Deposits} = 2154 \times 72 = 155,088
\]

### Step 5: Calculate the total interest earned.
The interest earned is the difference between the future value and the total deposits:
\[
\text{Interest} = 189,653.04 - 155,088 = 34,565.04
\]

So, the interest earned is approximately **$34,565.04**.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What if the interest rate changes to 7% compounded monthly?
2. How would the outcome differ with a quarterly compounding period?
3. How much would the interest be if you stopped the annuity after 3 years?
4. What would the total amount be if the deposit was increased by $100 monthly?
5. How does the future value change with a 5-year plan instead of 6?

**Tip:** Compounding frequency plays a crucial role in maximizing returns on an annuity. Monthly compounding yields more than annual compounding due to more frequent interest accumulation.

Calculate the future value of an annuity with monthly deposits of $2154 at an interest rate of 6.6% compounded monthly over 6 years. This guide provides step-by-step calculations for both the future value and the total interest earned. Suitable for advanced high school and college students.

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