Exercise 6 4 Solve the following problems: 1. Find the maturity value of P21,000 deposited at 9.5% compounded semi-annually for 3 years and 6 months? 2. Accumulate P95,500 for 7 years at 11 1/2% compounded annually. 3. Aster Atsumi borrowed P20,000 at 8% compounded quarterly. How much will she have to pay at the end of 5 years? 4. Find the compound interest earned if 70,000 is invested for 10 years at 6% compounded monthly? Using the formula F=P(1+i)n

To solve these compound interest problems, we'll use the compound interest formula:

\[
F = P(1 + i)^n
\]

Where:
- \( F \) is the maturity value (or future value),
- \( P \) is the principal (initial deposit or loan),
- \( i \) is the interest rate per period (annual interest rate divided by the number of compounding periods per year),
- \( n \) is the total number of compounding periods (compounding periods per year multiplied by the number of years).

### 1. **Find the maturity value of P21,000 deposited at 9.5% compounded semi-annually for 3 years and 6 months:**

- \( P = 21,000 \)
- Annual interest rate \( = 9.5\% = 0.095 \)
- Compounding is semi-annual, so \( i = \frac{0.095}{2} = 0.0475 \)
- Time is 3 years and 6 months, so in semi-annual periods \( n = 2 \times 3.5 = 7 \)

Using the formula \( F = P(1 + i)^n \):

\[
F = 21,000(1 + 0.0475)^7
\]

Let's calculate this.

### 2. **Accumulate P95,500 for 7 years at 11 1/2% compounded annually:**

- \( P = 95,500 \)
- Annual interest rate \( = 11.5\% = 0.115 \)
- Since it's compounded annually, \( i = 0.115 \)
- Time is 7 years, so \( n = 7 \)

Using the formula \( F = P(1 + i)^n \):

\[
F = 95,500(1 + 0.115)^7
\]

Let's calculate this.

### 3. **Aster Atsumi borrowed P20,000 at 8% compounded quarterly. How much will she have to pay at the end of 5 years?**

- \( P = 20,000 \)
- Annual interest rate \( = 8\% = 0.08 \)
- Compounded quarterly, so \( i = \frac{0.08}{4} = 0.02 \)
- Time is 5 years, so in quarterly periods \( n = 4 \times 5 = 20 \)

Using the formula \( F = P(1 + i)^n \):

\[
F = 20,000(1 + 0.02)^{20}
\]

Let's calculate this.

### 4. **Find the compound interest earned if P70,000 is invested for 10 years at 6% compounded monthly:**

Here, we'll find the maturity value first and then calculate the compound interest earned by subtracting the principal from the maturity value.

- \( P = 70,000 \)
- Annual interest rate \( = 6\% = 0.06 \)
- Compounded monthly, so \( i = \frac{0.06}{12} = 0.005 \)
- Time is 10 years, so in monthly periods \( n = 12 \times 10 = 120 \)

Using the formula \( F = P(1 + i)^n \):

\[
F = 70,000(1 + 0.005)^{120}
\]

Compound interest earned \( = F - P \).

Now, let's calculate all these results.Here are the results for the given problems:

1. **Maturity value for P21,000 deposited at 9.5% compounded semi-annually for 3 years and 6 months:**
   \[
   F = P29,060.13
   \]

2. **Maturity value for P95,500 accumulated over 7 years at 11.5% compounded annually:**
   \[
   F = P204,610.28
   \]

3. **Amount Aster Atsumi will have to pay after borrowing P20,000 at 8% compounded quarterly for 5 years:**
   \[
   F = P29,718.95
   \]

4. **Compound interest earned on P70,000 invested for 10 years at 6% compounded monthly:**
   - Maturity value: \( F = P127,357.77 \)
   - Compound interest earned: \( 127,357.77 - 70,000 = P57,357.77 \)

Let me know if you'd like further details or explanations.

Here are 5 related questions for further practice:
1. What is the maturity value of P15,000 invested at 7% compounded monthly for 4 years?
2. How much interest is earned on P80,000 compounded quarterly at 5% for 6 years?
3. Find the maturity value of P50,000 at 9% compounded annually for 10 years.
4. What is the difference in the final amount if P10,000 is compounded semi-annually vs. quarterly over 8 years at 6%?
5. If a person invests P5,000 at 10% compounded annually for 15 years, what will the future value be?

**Tip:** The more frequent the compounding, the higher the maturity value for the same interest rate and time period.

Learn how to solve compound interest problems including calculating the maturity value of P21,000 at 9.5% compounded semi-annually, P95,500 over 7 years at 11.5%, and more. This detailed guide applies the compound interest formula for real-world financial scenarios, suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation