Exercise 1.10 1. If Birr 1200 is invested at $$ 10 \% $$ simple interest per annum, then What is simple interest after 5 years? 2. What principal will bring Birr 637 interest at a rate of $$ 7 \% $$ in 2 years? 3. Find the simple interest rate for a loan where Birr 6000 is borrowed and amount owned after 5 months is Birr 7500 .

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Certainly! Let's tackle each of the three questions related to simple interest step by step.

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### **1. Simple Interest on Birr 1,200 at 10% per Annum for 5 Years**

**Given:**
- **Principal (P)** = Birr 1,200
- **Rate of Interest (R)** = 10% per annum
- **Time (T)** = 5 years

**Formula for Simple Interest (SI):**
$$ \text{SI} = \frac{P \times R \times T}{100} $$

**Calculation:**
$$
\begin{align*}
\text{SI} &= \frac{1,200 \times 10 \times 5}{100} \
&= \frac{60,000}{100} \
&= 600
\end{align*}
$$

**Answer:**  
The simple interest after 5 years is **Birr 600**.

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### **2. Finding the Principal that Yields Birr 637 Interest at 7% for 2 Years**

**Given:**
- **Interest (SI)** = Birr 637
- **Rate of Interest (R)** = 7% per annum
- **Time (T)** = 2 years

**We need to find the Principal (P).**

**Rearranged Formula for Principal:**
$$ P = \frac{\text{SI} \times 100}{R \times T} $$

**Calculation:**
$$
\begin{align*}
P &= \frac{637 \times 100}{7 \times 2} \
&= \frac{63,700}{14} \
&= 4,550
\end{align*}
$$

**Answer:**  
The principal required is **Birr 4,550**.

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### **3. Finding the Simple Interest Rate for a Loan of Birr 6,000 with Amount Owed Birr 7,500 after 5 Months**

**Given:**
- **Principal (P)** = Birr 6,000
- **Amount (A)** = Birr 7,500
- **Time (T)** = 5 months

**First, find the Simple Interest (SI):**
$$ \text{SI} = A - P $$
$$
\text{SI} = 7,500 - 6,000 = 1,500
$$

**Now, find the Rate (R).**

**Formula for Rate:**
$$ R = \frac{\text{SI} \times 100}{P \times T} $$

**Note:** Time should be in years.  
5 months = $$ \frac{5}{12} $$ years.

**Calculation:**
$$
\begin{align*}
R &= \frac{1,500 \times 100}{6,000 \times \frac{5}{12}} \
&= \frac{150,000}{6,000 \times 0.4167} \
&= \frac{150,000}{2,500} \
&= 60
\end{align*}
$$

**Answer:**  
The simple interest rate is **60% per annum**.

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**Summary of Answers:**
1. **Birr 600** simple interest after 5 years.
2. **Birr 4,550** principal needed.
3. **60%** simple interest rate.

If you have any further questions or need additional explanations, feel free to ask!
**Answers:** 1. **Birr 600** simple interest after 5 years. 2. **Birr 4,550** principal needed. 3. **60%** simple interest rate. If you have any more questions, feel free to ask!

Exercise 1.10

If Birr 1200 is invested at simple interest per annum, then What is
simple interest after 5 years?

What principal will bring Birr 637 interest at a rate of in 2 years?

Find the simple interest rate for a loan where Birr 6000 is borrowed and
amount owned after 5 months is Birr 7500 .

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