Suppose someone wants to accumulate 

​$45 comma 00045,000 

for a college fund over the next 15 years. Determine whether the following investment plans will allow the person to reach the goal. Assume the compounding and payment periods are the same.

The person deposits 

​$9090 

per month into an account with an APR of 

66​%.

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Part 1

Will the person meet the​ goal? Select the correct choice below and fill in the answer box to complete your choice.

To determine whether the person will meet the goal of accumulating $45,000 over 15 years by depositing $90 per month with an APR of 6%, we will use the **future value of an ordinary annuity formula**:

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

Where:
- $FV$ is the future value (the amount accumulated),
- $P$ is the monthly deposit ($90),
- $r$ is the annual interest rate (6%, or 0.06 as a decimal),
- $n$ is the number of times the interest is compounded per year (monthly means $n = 12$),
- $t$ is the number of years (15 years).

### Step 1: Input values into the formula
- $P = 90$
- $r = 0.06$
- $n = 12$
- $t = 15$

Now, I'll compute the future value $FV$.It seems like I can’t do more advanced data analysis right now. Please try again later.

You can follow these steps manually to calculate whether the investment will reach the goal:

1. **Insert values** into the future value formula:
   \[
   FV = 90 \times \left( \frac{(1 + \frac{0.06}{12})^{12 \times 15} - 1}{\frac{0.06}{12}} \right)
   \]
   
2. **Compute** the results to get the total amount accumulated over 15 years.

3. Compare this total to the target of $45,000.

If you have any questions, feel free to ask!

Here are 5 questions related to this:

1. How does compounding frequency affect the future value of an investment?
2. What is the difference between APR and APY in interest calculations?
3. How would the future value change if the interest rate were 8% instead of 6%?
4. What happens if the person misses a few monthly payments?
5. How is the future value formula derived from the basic compound interest formula?

**Tip:** The higher the compounding frequency, the more interest is earned over time!

Suppose someone wants to accumulate $45,000 for a college fund over the next 15 years. Determine whether the following investment plans will allow the person to reach the goal. Assume the compounding and payment periods are the same. The person deposits $90 per month into an account with an APR of 6%. Will the person meet the goal?

Learn how to calculate the future value of a college fund annuity by depositing $90 monthly into an account with a 6% APR over 15 years. This problem covers key financial concepts like compound interest and annuities, using the future value of an ordinary annuity formula. Suitable for students in Grades 11-12.

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