Find the accumulated value of ₱700 at the end of 10 years (a) at 8% compounded
annually (b) at 8% simple interest

To find the accumulated value of ₱700 at the end of 10 years, we'll calculate both (a) compound interest and (b) simple interest.

### (a) Compound Interest
For compound interest, the formula is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the accumulated amount
- \( P \) is the principal amount (₱700)
- \( r \) is the annual interest rate (8% or 0.08)
- \( n \) is the number of times the interest is compounded per year (annually, so \( n = 1 \))
- \( t \) is the time in years (10 years)

Plugging in the values:

\[
A = 700 \left(1 + \frac{0.08}{1}\right)^{1 \times 10} = 700 \left(1.08\right)^{10}
\]

Now, calculate \( (1.08)^{10} \):

\[
(1.08)^{10} \approx 2.1589
\]

So,

\[
A = 700 \times 2.1589 \approx 1,511.23
\]

The accumulated value at 8% compounded annually is approximately **₱1,511.23**.

### (b) Simple Interest
For simple interest, the formula is:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the accumulated amount
- \( P \) is the principal amount (₱700)
- \( r \) is the annual interest rate (8% or 0.08)
- \( t \) is the time in years (10 years)

Plugging in the values:

\[
A = 700 \times (1 + 0.08 \times 10) = 700 \times (1 + 0.8) = 700 \times 1.8 = 1,260
\]

The accumulated value at 8% simple interest is **₱1,260**.

### Summary
- **Compound Interest (8% compounded annually):** ₱1,511.23
- **Simple Interest (8% simple interest):** ₱1,260

Would you like any further details or explanations?

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Here are 8 related questions to expand on this topic:
1. How would the accumulated value change if the interest rate was 10% instead of 8%?
2. What if the interest was compounded semi-annually instead of annually?
3. How does the time period affect the difference between simple and compound interest?
4. Can you calculate the compound interest if the interest was compounded monthly?
5. How do you calculate the present value if you know the future value and interest rate?
6. What is the formula for continuous compounding interest?
7. How would the accumulated value be affected if the principal amount was increased to ₱1,000?
8. Can you explain the difference between nominal and effective interest rates?

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**Tip:** Always double-check the time period for compounding in compound interest calculations, as it significantly impacts the accumulated amount.

Learn how to calculate the accumulated value of ₱700 at the end of 10 years using compound and simple interest. Detailed step-by-step solutions provided for both types of interest calculations with an 8% interest rate.

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