Cassidy Hemlock spends $80 a month on doughnuts and coffee and is considering the advantages of quitting that habit. If Cassidy just turned 22 and deposits the $80 at the end of each month into a savings plan earning 5.85% compounded monthly, how much will she have in her savings plan at age 75, after her final deposit?

This problem involves calculating the future value of a series of regular monthly payments deposited into a savings plan that earns compound interest.

The future value $FV$ of an annuity (a series of regular payments) can be calculated using the following formula:

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

Where:
- $P$ is the regular monthly payment (in this case, \$80),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (months),
- $FV$ is the future value of the savings plan.

### Step-by-Step Solution:

1. **Identify the known values**:
   - Monthly payment $P = 80$ dollars,
   - Annual interest rate $5.85\%$,
   - Monthly interest rate $r = \frac{5.85\%}{12} = \frac{0.0585}{12} = 0.004875$,
   - Age now = 22, Age at final deposit = 75, so the number of years is $75 - 22 = 53$,
   - Number of months $n = 53 \times 12 = 636$.

2. **Substitute the values into the formula**:

\[
FV = 80 \times \frac{(1 + 0.004875)^{636} - 1}{0.004875}
\]

Now, let's calculate the future value.The future value of Cassidy Hemlock's savings plan at age 75, after making monthly deposits of $80 for 53 years at an interest rate of 5.85% compounded monthly, will be approximately **$345,310.87**.

Would you like further details on the calculation or have any other questions?

Here are some related questions you might find interesting:
1. How much interest alone is earned over the 53 years?
2. How would the savings change if the interest rate were higher or lower?
3. What if Cassidy started saving earlier, at age 18, instead of 22?
4. How much would Cassidy save if she increased her monthly deposit by $20 every 5 years?
5. How much would she have saved if the compounding was quarterly instead of monthly?

**Tip**: Starting to save earlier can significantly increase the total savings due to the power of compound interest.

Discover how much Cassidy Hemlock will save by depositing $80 monthly into a savings plan with 5.85% interest compounded monthly for 53 years. This real-world problem involves calculating the future value of an annuity using compound interest formulas. Suitable for advanced high school or college students.

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