Part A: Amount in the Retirement Account at Age 65

We are given:

• Quarterly deposit = $200
• Annual interest rate = 5%, compounded quarterly → Quarterly interest rate $i = \frac{5\%}{4} = 0.0125$
• Number of quarters from age 50 to 65 = $15 \text{ years} \times 4 \text{ quarters/year} = 60 \text{ quarters}$

The formula for the future value of an annuity (regular deposits) compounded periodically is:

$FV = P \times \frac{(1 + i)^n - 1}{i}$

Where:

• $P$ = Quarterly deposit = $200
• $i$ = Quarterly interest rate = 0.0125
• $n$ = Number of periods = 60 quarters

Substituting the values:

$FV = 200 \times \frac{(1 + 0.0125)^{60} - 1}{0.0125}$

Let's calculate that first.At the end of 65 years old, Bert and Bertha will have approximately $17,714.90 in their retirement account.

Part B: Size of Withdrawals from Age 65 to 80

We are given:

• The account balance at age 65 = $17,714.90
• Quarterly withdrawals for 15 years (from 65 to 80) → Number of quarters $= 15 \times 4 = 60$
• Quarterly interest rate $i = 0.0125$

The formula for calculating the periodic withdrawals from an account (annuity) is:

$W = \frac{FV \times i}{1 - (1 + i)^{-n}}$

Where:

• $W$ = Quarterly withdrawal amount
• $FV$ = Future value of the account = $17,714.90
• $i$ = Quarterly interest rate = 0.0125
• $n$ = Number of periods = 60 quarters

Now, let's calculate the withdrawal size.Bert and Bertha can withdraw approximately $421.44 per quarter from their retirement account for 15 years, starting 3 months after their last deposit at age 65.

Part C: Total Deposits, Total Withdrawals, and Total Interest

1. Total Deposits:

   • Quarterly deposit = $200
   • Number of quarters = 60 $\text{Total Deposits} = 200 \times 60 = 12,000$

2. Total Withdrawals:

   • Quarterly withdrawal = $421.44
   • Number of quarters = 60 $\text{Total Withdrawals} = 421.44 \times 60$

3. Total Interest: $\text{Total Interest} = \text{Total Withdrawals} - \text{Total Deposits}$

Let's calculate the total withdrawals and the total interest.### Summary of Results for Part C:

1. Total Deposits: $12,000
2. Total Withdrawals: $25,286.18
3. Total Interest Earned: $13,286.18

This means that Bert and Bertha deposited $12,000, withdrew $25,286.18, and earned a total of $13,286.18 in interest.

---

Do you need further details or clarification?

Here are 5 related questions:

1. How would the results change if the interest was compounded monthly instead of quarterly?
2. What happens if they decide to make monthly instead of quarterly deposits?
3. How does a change in the interest rate (say to 6%) affect their withdrawals?
4. Can the withdrawal amount be adjusted if they plan for a longer retirement period (e.g., until age 85)?
5. How does delaying their retirement by 5 years affect their future balance?

Tip: Regularly review and adjust your retirement contributions to align with your future goals and inflation.