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To solve this problem, we need to calculate the future value of a series of quarterly deposits ($21,000) that have been compounded at a 4.05% annual interest rate, compounded semi-annually over a period of 4 years.

Here's the breakdown:

1. **Determine Effective Interest Rate Per Compounding Period:**
   Since interest is compounded semi-annually, each compounding period is 6 months, and the annual interest rate is 4.05%.
   
   - Semi-annual interest rate = $ \frac{4.05\%}{2} = 2.025\% $ per 6 months.
   - Convert this to a decimal: $ 2.025\% = 0.02025 $.

2. **Number of Compounding Periods:**
   - The deposits are made quarterly, which is every 3 months, so there are 2 deposits per compounding period.
   - Over 4 years, there are $4 \times 4 = 16$ quarterly deposits.

3. **Calculate Future Value of Annuity (Quarterly Deposits):**
   We use the future value of an annuity formula for compounding interest:
   \[
   FV = P \times \frac{(1 + r)^n - 1}{r}
   \]
   where:
   - $ P = 21,000 $ (deposit amount),
   - $ r = 0.02025 $,
   - $ n = 16 $.

I'll calculate the future value based on these values.The total amount in the fund today is approximately **$392,185.72**.

Would you like further details on any steps or have additional questions?

Here are five related questions to deepen understanding:
1. How would the total change if the interest rate were compounded quarterly instead of semi-annually?
2. What if the team decided to increase the deposit amount each year by a certain percentage?
3. How much would the fund hold after an additional two years at the same deposit rate?
4. What would be the impact of a different interest rate on the final amount?
5. How does the frequency of compounding (monthly vs. semi-annual) affect the overall growth?

**Tip:** Compounding more frequently generally increases the future value due to interest being applied more often.

The Saskatchewan Roughriders started a rainy day savings fund 4 years ago to help pay for stadium improvements. At the beginning of every quarter, the team has deposited $21,000 into the fund, which has been earning 4.05% compounded semi-annually. How much money is in the fund today?

Learn how to calculate the future value of a rainy day fund with quarterly deposits of $21,000, compounded semi-annually at 4.05% over 4 years. This solution uses the future value of annuity formula and covers compound interest concepts, making it ideal for Grades 11-12.

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