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To solve this question, we can break it down into two parts: 

1. **Accumulation during the first three years** while deposits are being made each month.
2. **Growth over the final two years** when no further deposits are made.

Here’s how we proceed:

### Part 1: Accumulation of deposits for the first three years
Since R 2400 is deposited monthly for three years at an interest rate of 8% compounded monthly, we use the future value of an annuity formula:

\[
FV = P \cdot \frac{(1 + i)^n - 1}{i}
\]

where:
- \( P = 2400 \) (monthly deposit),
- \( i = \frac{8\%}{12} = 0.0066667 \) (monthly interest rate),
- \( n = 3 \times 12 = 36 \) (total number of deposits).

#### Calculating the Future Value after 3 years:

\[
FV = 2400 \cdot \frac{(1 + 0.0066667)^{36} - 1}{0.0066667}
\]

Calculating this gives us the accumulated amount after three years.

### Part 2: Growth over the next two years
After three years, the deposits stop, and the amount accumulated will continue to grow for another two years at the same interest rate (8% compounded monthly). Now we treat this amount as a lump sum and calculate its value after two more years.

The compound interest formula is:

\[
A = FV \cdot (1 + i)^m
\]

where:
- \( FV \) is the amount from Part 1,
- \( i = 0.0066667 \),
- \( m = 2 \times 12 = 24 \) (compounding periods for two additional years).

### Final Calculation
Using these formulas and steps will yield the total amount in the account after five years. Let me know if you'd like me to carry out the exact calculations or if you have any questions about the process!

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**Additional Questions:**

1. How would the final amount change if deposits continued for the full five years?
2. What would be the effect of changing the compounding frequency to quarterly or annually?
3. How much would be accumulated if the deposit amount was R 3000 instead of R 2400?
4. What would happen if the interest rate was 6% instead of 8%?
5. How does compound interest differ from simple interest over the same period?

**Tip:** Remember that compound interest grows faster with more frequent compounding periods due to "interest on interest."

Suppose R 2 400 is placed in a savings account at the end of each month for three years and thereafter no further deposits are made. How much is in the account after five years if the interest rate is 8% compounded monthly?

Learn how to determine the future savings balance after making monthly deposits of R 2 400 for three years at an 8% interest rate compounded monthly, followed by two years of compounded growth without deposits. Ideal for students in Grades 11-12, covering annuities and compound interest.

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