Sue wants to leave her grandson a nice inheritance. She has decided to deposit

$200.00​ each month into an ordinary annuity that earns
4.3% compounded monthly.

How much will be in the account after
30 years?  Round your final answer to the nearest cent.  Assume the interest rate stays the same while the account is open.

To calculate the future value of an ordinary annuity, we can use the formula:

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

where:
- $FV$ is the future value of the annuity
- $P$ is the monthly payment (which is $200.00 in this case)
- $r$ is the monthly interest rate
- $n$ is the total number of payments

### Step 1: Identify the variables
- Monthly payment $P = 200.00$
- Annual interest rate $ = 4.3\%$
- Monthly interest rate $r = \frac{4.3\%}{12} = \frac{0.043}{12} = 0.0035833$
- Number of years $ = 30$
- Total number of payments $n = 30 \times 12 = 360$

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

\[
FV = 200 \times \frac{(1 + 0.0035833)^{360} - 1}{0.0035833}
\]

Let's calculate the future value.The future value of the annuity after 30 years will be **$146,479.25** when rounded to the nearest cent.

Do you have any further questions or would you like more details on the calculation?

Here are 8 related questions:
1. How would the future value change if the interest rate increased to 5%?
2. What if Sue deposits $300 instead of $200 per month?
3. How much interest will Sue have earned over the 30 years?
4. What is the formula for calculating the present value of an annuity?
5. How would the future value change if the compounding frequency was quarterly instead of monthly?
6. What is the effect of starting the annuity 5 years later, with the same monthly deposit?
7. How would the future value change if Sue decides to stop making payments after 20 years?
8. How does this future value compare to that of a simple savings account with the same interest rate?

**Tip:** The power of compound interest grows significantly with time; starting early can greatly increase the final amount.

Learn how to calculate the future value of an ordinary annuity with monthly deposits using compound interest. Get the solution for Sue's scenario: depositing $200 monthly at 4.3% interest compounded monthly for 30 years.

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