Suppose you want to withdraw $1500 at the end of each year for five years from an account paying 6% compounded annually. How much must you deposit at the beginning of the annuity?

Question 1 options:

$7486.00


$7950.00


$7486.52


$7050.00


$6318.55 

This problem involves finding the present value of an ordinary annuity. The present value of an annuity formula is given by:

\[
PV = \dfrac{R \left(1 - (1 + i)^{-n}\right)}{i}
\]

Where:
- $ PV $ is the present value (the amount to deposit now),
- $ R $ is the regular withdrawal amount (in this case, $1500),
- $ i $ is the interest rate per period (6% or 0.06),
- $ n $ is the number of periods (5 years).

Let's substitute the values into the formula:

\[
PV = \dfrac{1500 \left(1 - (1 + 0.06)^{-5}\right)}{0.06}
\]

I'll calculate this step-by-step.The present value, or the amount that must be deposited at the beginning of the annuity, is approximately **$6318.55**.

Thus, the correct answer is:

**$6318.55**

Would you like any further details or have any questions?

Here are five related questions for further exploration:
1. How would the deposit change if the interest rate were 5% instead of 6%?
2. What would be the future value of the same annuity after five years?
3. How does the formula change if payments were made at the beginning of each year (annuity due)?
4. How would the solution change if withdrawals were made monthly instead of annually?
5. What is the total amount withdrawn over the five years?

**Tip:** The higher the interest rate, the lower the initial deposit needed to achieve the same withdrawals.

Suppose you want to withdraw $1500 at the end of each year for five years from an account paying 6% compounded annually. How much must you deposit at the beginning of the annuity?

Learn how to calculate the present value needed to withdraw $1500 annually for five years from an account with 6% compounded interest. This detailed solution covers the present value of an ordinary annuity, making it suitable for Grades 11-12 and college students.

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