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Part 1

​Recently, More Money 4U offered an annuity that pays

6.9 %6.9%

compounded monthly. If

$ 1 comma 219$1,219

is deposited into this annuity every​ month, how much is in the account after

77

​years? How much of this is​ interest?

To calculate the total amount in the account after 7 years for the given annuity, we will use the formula for the future value of an annuity compounded monthly:

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

Where:
- $FV$ is the future value of the annuity (the amount in the account after 7 years),
- $P$ is the monthly deposit (\$1,219),
- $r$ is the annual interest rate (6.9% or 0.069),
- $n$ is the number of times the interest is compounded per year (12 for monthly compounding),
- $t$ is the number of years (7).

Now, let's plug the numbers into the formula:

\[
FV = 1219 \times \frac{(1 + \frac{0.069}{12})^{12 \times 7} - 1}{\frac{0.069}{12}}
\]

### Step 1: Calculate the monthly interest rate
\[
r/n = \frac{0.069}{12} = 0.00575
\]

### Step 2: Calculate the exponent
\[
nt = 12 \times 7 = 84
\]

Now, let's compute the future value.The total amount in the account after 7 years will be approximately \$131,162.11.

### To calculate how much of this is interest, we subtract the total contributions from the future value.

The total contributions are calculated as:

\[
\text{Total Contributions} = P \times n \times t = 1219 \times 12 \times 7
\]

Let's calculate how much is interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

To continue from where we left off, here's how you can calculate the total contributions and interest:

1. **Total Contributions**:
\[
\text{Total Contributions} = 1219 \times 12 \times 7 = 102,036
\]

2. **Interest**:
\[
\text{Interest} = \text{Future Value} - \text{Total Contributions} = 131,162.11 - 102,036 = 29,126.11
\]

So, after 7 years:
- Total contributions: \$102,036
- Interest earned: \$29,126.11

Would you like more details or have any questions about this?

Here are 5 related questions:
1. What if the interest rate was compounded quarterly instead of monthly?
2. How would the future value change if you invested for 10 years instead of 7?
3. What happens if the monthly deposit was increased to \$1,500?
4. How can you calculate the present value of this annuity if it were instead paid out over time?
5. What is the difference between simple interest and compound interest in this context?

**Tip:** Always double-check your calculations when working with compounded interest to ensure accuracy.

Recently, More Money 4U offered an annuity that pays 6.9% compounded monthly. If $1,219 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest?

Discover how to calculate the future value of an annuity with monthly deposits of $1,219 over 7 years at an interest rate of 6.9% compounded monthly. Learn the step-by-step process to find the total amount and interest earned. Suitable for high school students in Grades 10-12.

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