To determine the accumulated value of your retirement fund, we need to consider the two phases of interest rates: 4.5% for the first 11 years and 4.25% for the remaining 7 years. We’ll break down the calculation into these two parts and calculate the future value at the end of each phase.

Given Data:

• Initial deposit (P₀): €12,500
• Annual contributions (P): €9,000 (at the end of each year)
• Interest rate (first 11 years): 4.5% compounded annually
• Interest rate (last 7 years): 4.25% compounded annually

Step 1: Calculate the accumulated value at the end of 11 years (4.5% interest)

1. Initial Deposit Growth (First 11 years):
   The initial deposit grows with interest for 11 years without any further contributions.

   $FV_{\text{initial}} = P_0 \times (1 + r)^{11} = 12,500 \times (1 + 0.045)^{11}$

2. Annual Contributions Growth (First 11 years):
   Each of the €9,000 contributions at the end of each year grows with interest for the remaining years in this 11-year period.

   Using the future value of an annuity formula:

   $FV_{\text{annuity}} = P \times \frac{(1 + r)^{n} - 1}{r} = 9,000 \times \frac{(1 + 0.045)^{11} - 1}{0.045}$

   Adding the two components gives us the total fund value at the end of 11 years.

Step 2: Calculate the accumulated value at the end of 18 years (additional 7 years at 4.25%)

1. Value Grown in Second Period (7 years at 4.25%):
   Now, the accumulated fund from Step 1 will grow at 4.25% for the remaining 7 years.

   $FV_{\text{total}} = \text{Fund Value After 11 Years} \times (1 + 0.0425)^7$

2. Additional Contributions for Last 7 Years: Contributions of €9,000 continue each year during these 7 years, and each contribution will grow with 4.25% interest for the remaining years within this period.

   $FV_{\text{last 7 years}} = P \times \frac{(1 + r)^{n} - 1}{r} = 9,000 \times \frac{(1 + 0.0425)^7 - 1}{0.0425}$

Finally, adding these components will give the total accumulated value of the fund at the end of 18 years. Let’s calculate these values explicitly.The accumulated value of your retirement fund at the end of 18 years is approximately €265,478.04.

Would you like a breakdown of these calculations or have further questions?

Here are some related questions:

1. How does the difference in interest rates impact the final amount?
2. How would the final value change if the annual contribution were increased?
3. What if contributions started at a different year—how would that affect the total?
4. How much impact does compounding frequency (annually vs. semi-annually) have?
5. What would be the effect of adding a lump sum in the last few years?

Tip: Consistently reviewing interest rates for retirement funds can help maximize future returns.