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A child is given savings account with 2000. A further 500 is deposited in the account at the end of each year. assuming an annual interest rate of 6%, calculate the value of the account, a. at the end of 10 years, b. at the end of 20 years. kerjakan dengan rumus dari gambar yang saya berikan!

To calculate the value of the account using the formula provided in the image:

\[
V_t = P_0 (1 + i)^t + A_0 \frac{(1 + i)^t - 1}{i}
\]

where:
- \( V_t \) is the value of the account at time \( t \),
- \( P_0 \) is the initial principal (initial deposit),
- \( A_0 \) is the annual deposit added at the end of each year,
- \( i \) is the interest rate per period,
- \( t \) is the number of years.

### Given Values
- \( P_0 = 2000 \)
- \( A_0 = 500 \)
- \( i = 0.06 \) (since the annual interest rate is 6%)
  
We will calculate the account value at:
1. **\( t = 10 \) years**
2. **\( t = 20 \) years**

### Step 1: Calculate \( V_{10} \)

Substitute \( t = 10 \) into the formula:

\[
V_{10} = 2000 (1 + 0.06)^{10} + 500 \frac{(1 + 0.06)^{10} - 1}{0.06}
\]

### Step 2: Calculate \( V_{20} \)

Substitute \( t = 20 \) into the formula:

\[
V_{20} = 2000 (1 + 0.06)^{20} + 500 \frac{(1 + 0.06)^{20} - 1}{0.06}
\]

I'll compute these values now.The calculated values of the account are as follows:

1. At the end of **10 years**, \( V_{10} \approx 10,172.09 \).
2. At the end of **20 years**, \( V_{20} \approx 24,807.07 \).

Would you like a detailed breakdown of each step in the calculation, or do you have any questions?

Here are some related questions to deepen understanding:

1. How would the account value change if the interest rate were compounded monthly rather than annually?
2. What would the future value be if the annual deposit amount increased to 600 instead of 500?
3. How does the initial deposit (\( P_0 \)) impact the total amount after 10 and 20 years?
4. What is the effect of doubling the annual deposit (\( A_0 \)) on the value after 20 years?
5. Can this formula be adapted to model quarterly deposits instead of annual?

**Tip:** In compound interest calculations, increasing the frequency of deposits or the interest compounding period typically yields higher returns due to more frequent growth adjustments.

A child is given a savings account with 2000. A further 500 is deposited in the account at the end of each year. Assuming an annual interest rate of 6%, calculate the value of the account, a. at the end of 10 years, b. at the end of 20 years.

Learn how to calculate the future value of a savings account with an initial deposit of 2000, annual deposits of 500, and an interest rate of 6%. Find out the account value at the end of 10 and 20 years using compound interest and annuity formulas.

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