Kelly invested his savings of $1,175 in a savings account that was earning simple interest at 2.22% p.a. He also invested $3,325 in his friend's business at 0.20% p.m.

**a.** What is the interest rate per month that is equivalent to 2.22% p.a.?

To convert an annual interest rate to a monthly interest rate under simple interest, we divide the annual rate by 12 (the number of months in a year).

### Given Values
- Annual interest rate (r): 2.22%

### Calculation
1. **Convert annual percentage rate to decimal form**:
   \[ r_{\text{annual}} = \frac{2.22}{100} = 0.0222 \]

2. **Calculate the equivalent monthly interest rate**:
   \[ r_{\text{monthly}} = \frac{r_{\text{annual}}}{12} \]

   \[ r_{\text{monthly}} = \frac{0.0222}{12} \]

   \[ r_{\text{monthly}} \approx 0.00185 \]

3. **Convert back to percentage form**:
   \[ r_{\text{monthly\%}} = 0.00185 \times 100 \]

   \[ r_{\text{monthly\%}} \approx 0.185\% \]

### Conclusion
The interest rate per month equivalent to 2.22% per annum is approximately **0.185%** per month.

Would you like more details or have any questions on this? Here are some additional questions you might consider:

1. What is the total interest earned after 1 year from both investments?
2. How much interest does Kelly earn from the savings account after 6 months?
3. What would the monthly interest rate be if the annual rate was 3.5% p.a.?
4. How much will Kelly's investment in the business be worth after 1 year?
5. What is the difference in total interest earned between the two investments after 1 year?

**Tip:** When comparing investments with different compounding periods, always convert rates to a common period (like monthly or annually) for an accurate comparison.

Learn how to convert an annual interest rate of 2.22% p.a. to its equivalent monthly interest rate using simple interest calculations. This problem involves understanding the concept of simple interest and converting annual rates to monthly rates. Suitable for high school students and anyone interested in financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation