Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses. The account pays .39 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next four years?

To determine how much you need in your bank account today to cover the quarterly withdrawals, we can use the **present value of an annuity** formula. Since the withdrawals are periodic, and there's a constant interest rate, the present value of the series of withdrawals can be calculated using the formula for the present value of an ordinary annuity.

The formula for the present value of an ordinary annuity is:

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

Where:
- $PV$ is the present value (the amount you need in the account today).
- $P$ is the quarterly payment (the amount you will withdraw each quarter), which is $1,700.
- $r$ is the quarterly interest rate, which is 0.39% (or 0.0039 in decimal form).
- $n$ is the total number of quarters over which withdrawals will be made. Since the withdrawals are over 4 years and there are 4 quarters in a year, $n = 4 \times 4 = 16$.

Now, we can calculate:

\[
PV = 1700 \times \left( 1 - (1 + 0.0039)^{-16} \right) / 0.0039
\]

Let me calculate this for you.You would need approximately **$26,319.03** in your account today to cover your quarterly withdrawals of $1,700 over the next four years, given the 0.39% quarterly interest rate.

Would you like more details on this calculation, or do you have any further questions?

Here are 5 related questions that might expand your understanding:
1. How would the amount change if the interest rate were higher?
2. What if the withdrawals started immediately instead of after 3 months?
3. How does the number of withdrawal periods affect the total amount required?
4. What is the impact of making smaller, more frequent withdrawals?
5. How does compound interest influence the calculation in different scenarios?

**Tip:** Always ensure to adjust your calculations for the frequency of compounding when dealing with interest rates.

Learn how to calculate the amount needed in a bank account today to withdraw $1,700 quarterly for the next four years at a 0.39% interest rate. This example uses the present value of an annuity formula and illustrates key financial concepts like time value of money and annuities. Perfect for undergraduate finance students or advanced high school math learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation