Kashundra Jones plans a lump sum deposit so that she can withdraw 3,000 dollars at the end of each quarter for 10 years from an account that earns 10% interest per year compounded quarterly. What lump sum amount must she deposit now?

Introduction / Context:
This is another present value of an ordinary annuity question but with quarterly compounding. Kashundra wants to make regular withdrawals while interest accrues more frequently than annually, so the quarterly rate and the total number of quarters must be used in the calculation.

Given Data / Assumptions:

• Regular withdrawal R = 3,000 dollars at the end of each quarter.
• Nominal annual interest rate = 10%, compounded quarterly.
• Quarterly rate i = 10% / 4 = 2.5% = 0.025.
• Withdrawal horizon = 10 years, so n = 10 * 4 = 40 quarters.
• Withdrawals are at the end of each quarter (ordinary annuity).

Concept / Approach:
The present value of an ordinary annuity with periodic rate i and n periods is:
PV = R * (1 - (1 + i)^(-n)) / i Here PV is the lump sum required today so that, when the account grows at rate i each quarter, it will exactly fund the planned withdrawals.

Step-by-Step Solution:
Step 1: Set i = 0.025 and n = 40. Step 2: Compute (1 + i)^(-n) = (1.025)^(-40). Step 3: Evaluate the annuity factor: (1 - (1.025)^(-40)) / 0.025. Step 4: Multiply this factor by R = 3000. Step 5: The result gives PV ≈ 75,308.33 dollars. This is the amount that must be on deposit today to allow the desired withdrawals.

Verification / Alternative Check:
Total planned withdrawals equal 3,000 * 40 = 120,000 dollars. Since some of this total comes from interest, the initial deposit must be less than 120,000 dollars. A value around 75,000 dollars is reasonable because the account has 10 years of growth with relatively high interest.

Why Other Options Are Wrong:
Options B, C, and E (70,000; 65,000; 60,000 dollars) are all below the accurately calculated present value and would not produce enough money to fund all payments.
Option D (80,000 dollars) is higher than necessary and would leave unused balance if withdrawals proceeded as described.

Common Pitfalls:
Learners sometimes use the annual rate directly instead of converting to a quarterly rate, which yields a wrong answer. Another mistake is to treat the quarterly withdrawals as yearly withdrawals by using n = 10 instead of 40, which significantly miscalculates the present value.

Final Answer:
Kashundra must deposit approximately 75,308.33 dollars now.