You want to be able to withdraw $35,000 each year for 15 years. Your account earns 7% interest. How much do you need in your account at the beginning?

To determine how much you need in your account at the beginning to be able to withdraw $35,000 each year for 15 years, earning 7% interest, we use the formula for the **present value of an annuity**:

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

Where:
- $ PV $ is the present value (the amount you need at the beginning),
- $ P $ is the annual withdrawal ($35,000),
- $ r $ is the interest rate per period (7% or 0.07),
- $ n $ is the number of periods (15 years).

Let's calculate this:

\[
PV = 35,000 \times \left( \frac{1 - (1 + 0.07)^{-15}}{0.07} \right)
\]

I’ll compute the result for you.You will need approximately **$318,777** in your account at the beginning to withdraw $35,000 each year for 15 years, assuming a 7% annual interest rate.

Would you like any additional details or have any questions?

Here are 5 related questions to consider:
1. How does the interest rate affect the required initial amount?
2. What if the withdrawal period was 20 years instead of 15?
3. How would the calculation change with quarterly compounding?
4. What if you wanted to withdraw $40,000 instead of $35,000?
5. How does inflation affect the value of annual withdrawals over time?

**Tip:** The present value of an annuity decreases as the interest rate increases, meaning you need less initial investment for higher rates.

Find out how to calculate the amount needed in your account to withdraw $35,000 per year for 15 years, assuming a 7% interest rate. This detailed solution walks you through the present value of an annuity formula, covering concepts like interest rates and time value of money.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation