Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity.
​$700 invested monthly for 35 years at a 4.5​% interest rate compounded monthly
Upper A equals StartStartFraction p left bracket left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript n times t Baseline minus 1 right bracket OverOver StartFraction r Over n EndFraction EndEndFraction
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Part 1
The accumulated amount will be ​$

enter your response here.

The formula for the accumulated amount of an ordinary annuity is given by:

\[
A = P \left[ \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}} \right]
\]

Where:
- $ A $ is the accumulated amount.
- $ P $ is the periodic payment (in this case, \$700).
- $ r $ is the annual interest rate (4.5% = 0.045).
- $ n $ is the number of compounding periods per year (monthly compounding, so $ n = 12 $).
- $ t $ is the number of years (35 years).

Now, let's plug in the values:
- $ P = 700 $
- $ r = 0.045 $
- $ n = 12 $
- $ t = 35 $

\[
A = 700 \left[ \frac{\left(1 + \frac{0.045}{12}\right)^{12 \times 35} - 1}{\frac{0.045}{12}} \right]
\]

I'll calculate the accumulated amount next.The accumulated amount in the annuity after 35 years will be approximately **\$712,419.37**.

Would you like more details or have any further questions?

Here are five related questions for deeper understanding:
1. What would be the accumulated amount if the interest rate was 5% instead of 4.5%?
2. How does the accumulated amount change if the investment is made quarterly instead of monthly?
3. What happens to the accumulated amount if the investment period is reduced to 30 years?
4. How does increasing the monthly payment to \$800 affect the final amount?
5. Can you calculate the future value of a similar annuity with continuous compounding?

**Tip:** Small changes in interest rates can significantly affect the accumulated amount over long periods due to the compounding effect.

Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity. $700 invested monthly for 35 years at a 4.5% interest rate compounded monthly. The accumulated amount will be $____.

Find out how to calculate the accumulated amount for a $700 monthly annuity invested over 35 years at a 4.5% interest rate compounded monthly. This detailed explanation covers key financial math concepts like the ordinary annuity formula and compound interest. Suitable for advanced high school or college students.

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