A college student spends $55 per month on cigarettes. She has decided to stop
smoking and invest the $55 per month in a savings account at 4.8% interest
compounded monthly. What will the account be worth after 40 years?

To calculate the future value of the student's savings after 40 years, we'll again use the future value of an annuity formula:

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

Where:
- $ P = 55 $ dollars (monthly investment),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (number of months).

Given:
- Annual interest rate $ = 4.8\% $ or $ 0.048 $ as a decimal.
- Monthly interest rate $ r = \frac{0.048}{12} = 0.004 $.
- Number of months $ n = 40 \times 12 = 480 $.

Now, we'll calculate the future value.The account will be worth approximately **$79,679.68** after 40 years if the student invests $55 per month at an interest rate of 4.8% compounded monthly.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How much interest will the student earn over the 40 years?
2. What would be the future value if the interest rate were 6% instead of 4.8%?
3. How would the savings change if the student invested $100 per month instead of $55?
4. What would be the value of the account after 30 years instead of 40?
5. How much would the student need to invest monthly to reach $100,000 in 40 years?

**Tip:** Small monthly savings, when compounded over long periods, can grow significantly due to the power of compound interest.

Explore how to calculate the future value of savings by investing $55 monthly with a 4.8% interest rate compounded monthly. After 40 years, the account will be worth approximately $79,679.68. Learn about compound interest and annuities in financial mathematics.

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