The North Carolina Education Lottery has a drawing for the PowerBall twice a week and each ticket costs $2. Chris considers buying a ticket for every drawing. At 4 weeks per month, he would be spending about $16 each month. After taking a course in Quantitative Literacy, Chris also considers depositing that $16 into an account with an APR of 6.7% compounded monthly.

How much would Chris have in his savings account after 6 years? (Round to the nearest cent.)

To calculate how much Chris would have in his savings account after 6 years, we can use the future value of an ordinary annuity formula, where regular deposits are made and interest is compounded monthly.

The formula for the future value of an ordinary annuity is:

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

where:
- $ FV $ is the future value of the annuity.
- $ PMT $ is the monthly deposit amount ($16).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the total number of deposits (months).

Given:
- Annual interest rate (APR) = 6.7%, so the monthly interest rate $ r $ = 6.7% / 12 / 100 = 0.005583.
- Number of years = 6, so the number of months $ n $ = 6 * 12 = 72.

Now, substituting these values into the formula:

\[ FV = 16 \times \frac{(1 + 0.005583)^{72} - 1}{0.005583} \]

First, calculate $ (1 + r)^n $:

\[ (1 + 0.005583)^{72} = 1.005583^{72} \approx 1.448027 \]

Now, calculate $ FV $:

\[ FV = 16 \times \frac{1.448027 - 1}{0.005583} \]
\[ FV = 16 \times \frac{0.448027}{0.005583} \]
\[ FV = 16 \times 80.262 \]
\[ FV \approx 1284.19 \]

So, after 6 years, Chris would have approximately $1,284.19 in his savings account.

Would you like more details or have any questions?

Here are 5 questions you might consider asking next:
1. How does the compounding frequency affect the final amount in a savings account?
2. What are some effective strategies for increasing savings over time?
3. How would different interest rates impact Chris's savings after 6 years?
4. What is the impact of inflation on the future value of savings?
5. How does an ordinary annuity differ from an annuity due in terms of savings?

**Tip:** Consider using a financial calculator or spreadsheet to easily compute future values for different savings scenarios and interest rates.

Learn how to calculate savings over 6 years with compound interest and monthly deposits. Chris considers depositing $16 monthly into an account with an APR of 6.7% compounded monthly. After 6 years, find out how much Chris would have saved.

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