Derek will deposit $366.00 per year into an account starting today and ending in year 22.00. The account that earns 7.00%. How much will be in the account 22.0 years from today?



This is a future value problem involving an annuity due, where Derek is making equal annual deposits at the beginning of each period. The account earns 7% interest annually, and we need to find how much will be in the account after 22 years.

### Formula:
The future value $ FV $ of an annuity due can be calculated using the formula:

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

Where:
- $ P $ is the annual payment (366.00),
- $ r $ is the annual interest rate (7% or 0.07),
- $ n $ is the number of payments (22 years).

### Step-by-step calculation:

1. $ P = 366.00 $
2. $ r = 0.07 $
3. $ n = 22 $

Let's calculate the future value.

The future value of Derek's account 22 years from today will be approximately **$19,191.63**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How does the calculation change if the interest rate is compounded monthly instead of annually?
2. What if Derek deposited $500 per year instead of $366?
3. How much would Derek have after 22 years if he made end-of-year deposits instead of beginning-of-year deposits?
4. What is the total amount of interest earned over the 22 years?
5. How would the future value be affected if the account only earned 5% interest?

**Tip:** An annuity due gives slightly higher returns than an ordinary annuity because each payment is invested for an additional period.

Derek will deposit $366.00 per year into an account starting today and ending in year 22. The account that earns 7.00%. How much will be in the account 22.0 years from today?

Calculate the future value of an annuity due where Derek deposits $366 annually for 22 years with a 7% interest rate. Learn key concepts like annuity due, compound interest, and the future value formula. Ideal for students in Grades 10-12.

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