11. Accumulate P12,000 for 6 months at: a) 5.75% b) 10% c) 15% te is: 12. How long will it take for 21,000 at 9% simple interest to earn: a) 5,600 b) P6,000 c) 7,000 0. ts 13. Find the present value, if money earns 200 at the rate of 7% for: a) 60 days b) 3 months c) 5 years 14. Diana wants to earn $200 on the P12,000 that she lend for 2 and 1 half months. What simple interest rate must she give in order to earn the said amount? 15. If 12,500 was borrowed at 8% simple interest, how much will the interest be after 3 and 1 half years?

Let's solve each problem step-by-step.

### Problem 11: Accumulate P12,000 for 6 months at different interest rates

To find the accumulated amount, we need to use the formula for the **Future Value (FV)** under simple interest:

\[
FV = P \times \left(1 + \frac{r \times t}{100}\right)
\]

where:
- $ P = 12,000 $ (principal)
- $ r $ is the interest rate
- $ t = 6/12 = 0.5 $ years (since 6 months is half a year)

Let's calculate the future value for each interest rate:

#### a) At 5.75% interest rate:

\[
FV = 12,000 \times \left(1 + \frac{5.75 \times 0.5}{100}\right)
\]

\[
FV = 12,000 \times \left(1 + \frac{2.875}{100}\right)
\]

\[
FV = 12,000 \times (1 + 0.02875)
\]

\[
FV = 12,000 \times 1.02875 = 12,345
\]

#### b) At 10% interest rate:

\[
FV = 12,000 \times \left(1 + \frac{10 \times 0.5}{100}\right)
\]

\[
FV = 12,000 \times (1 + 0.05)
\]

\[
FV = 12,000 \times 1.05 = 12,600
\]

#### c) At 15% interest rate:

\[
FV = 12,000 \times \left(1 + \frac{15 \times 0.5}{100}\right)
\]

\[
FV = 12,000 \times (1 + 0.075)
\]

\[
FV = 12,000 \times 1.075 = 12,900
\]

### Problem 12: Time to earn a certain interest with simple interest

The formula for simple interest is:

\[
I = P \times \frac{r \times t}{100}
\]

Rearranging to solve for time $ t $:

\[
t = \frac{I \times 100}{P \times r}
\]

where:
- $ P = 21,000 $ (principal)
- $ r = 9\% $ (interest rate)

Let's calculate the time for each interest amount:

#### a) For P5,600:

\[
t = \frac{5,600 \times 100}{21,000 \times 9}
\]

\[
t = \frac{560,000}{189,000} \approx 2.96 \text{ years}
\]

#### b) For P6,000:

\[
t = \frac{6,000 \times 100}{21,000 \times 9}
\]

\[


Learn how to calculate future values and time required using simple interest. Solve problems like accumulating P12,000 over 6 months at different interest rates and determining time to earn specific amounts at 9% interest. Suitable for high school students.

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