Derek will deposit $157.00 per year into an account starting today and ending in year 10.00. The account that earns 5.00%. How much will be in the account 10.0 years from today?

This problem involves an annuity due, where Derek makes a series of deposits starting today and ending in year 10, with interest being compounded annually at a rate of 5%.

The formula for the future value of an annuity due is given by:

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

Where:
- $ P $ = annual deposit = \$157.00
- $ r $ = interest rate per period = 5% = 0.05
- $ n $ = number of deposits = 10 years

Let's compute this step-by-step.The amount in the account after 10 years will be approximately \$2,073.47.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the future value if Derek deposits \$200 annually instead?
2. How would the total change if the interest rate was 6%?
3. What happens if Derek deposits for 15 years instead of 10?
4. How much interest will Derek earn over the 10 years?
5. What if Derek makes the first deposit one year from now instead of today?

**Tip:** Annuity due payments grow faster than ordinary annuities due to the extra interest earned on each payment starting immediately.

Derek will deposit $157.00 per year into an account starting today and ending in year 10. The account that earns 5%. How much will be in the account 10 years from today?

Calculate the future value of an annuity due where Derek deposits $157 per year for 10 years into an account with a 5% annual interest rate. Learn how the formula for annuities can help determine the amount in the account after 10 years. This problem explores annuities, compound interest, and the time value of money, suitable for high school students in Grades 10-12.

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