At what nominal rate compounded semi-annually will PhP15,000 accumulate to PhP20,000 in 10 years?
2.88%
0.0288%
28.8%
0.288%

To find the nominal rate compounded semi-annually that will accumulate PhP15,000 to PhP20,000 in 10 years, we can use the formula for compound interest:

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

Where:
- \( A \) = future value (PhP20,000)
- \( P \) = present value (PhP15,000)
- \( r \) = nominal interest rate (annual)
- \( n \) = number of compounding periods per year (2 for semi-annual)
- \( t \) = number of years (10)

Rearranging the formula to solve for \( r \):

1. Substitute the values into the formula:

\[
20,000 = 15,000 \left(1 + \frac{r}{2}\right)^{2 \times 10}
\]

2. Divide both sides by 15,000:

\[
\frac{20,000}{15,000} = \left(1 + \frac{r}{2}\right)^{20}
\]

\[
\frac{4}{3} \approx 1.3333
\]

3. Take the 20th root of both sides:

\[
1 + \frac{r}{2} = \left(\frac{4}{3}\right)^{\frac{1}{20}}
\]

4. Calculate \( \left(\frac{4}{3}\right)^{\frac{1}{20}} \):

\[
1 + \frac{r}{2} \approx 1.0147
\]

5. Solve for \( r \):

\[
\frac{r}{2} \approx 0.0147 \implies r \approx 0.0294 \text{ or } 2.94\%
\]

None of the options match exactly, but 2.88% is the closest option provided. Therefore, the answer is **2.88%**.

Would you like further details or have any questions? Here are some related questions for you:

1. How does the compounding frequency affect the accumulated amount?
2. What is the formula for calculating compound interest?
3. How would the rate change if compounded annually instead of semi-annually?
4. What are the implications of a higher nominal rate on the future value?
5. Can you explain the concept of effective interest rate? 

**Tip:** Always compare the effective rate when considering different compounding periods.

At what nominal rate compounded semi-annually will PhP15,000 accumulate to PhP20,000 in 10 years? 2.88% 0.0288% 28.8% 0.288%

Discover how to determine the nominal interest rate that allows PhP15,000 to grow to PhP20,000 over 10 years with semi-annual compounding. This example uses the compound interest formula to find the closest solution, demonstrating step-by-step calculations for understanding interest rates.

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