1. **Problem a:** Ellen deposited money on 3 January 2020 and earned RM8,157.20 by 7 May 2020 at a 5.8% annual simple interest rate. Find the initial deposit. 2. Calculate the time period from 3 January to 7 May 2020. January 3 to May 7 is approximately 4 months and 4 days. Approximating time in years: $$ t = \frac{4 \text{ months} + 4 \text{ days}}{12 \times 30} = \frac{4 + \frac{4}{30}}{12} = \frac{4.133}{12} \approx 0.3444 \text{ years}$$ 3. Use the simple interest formula: $$ I = P \times r \times t $$ Where: - $I = 8157.20$ - $r = 5.8\% = 0.058$ - $t = 0.3444$ 4. Solve for principal $P$: $$ P = \frac{I}{r \times t} = \frac{8157.20}{0.058 \times 0.3444} = \frac{8157.20}{0.019975} \approx 408155.54 $$ 5. **Answer:** Ellen's initial deposit was approximately 408155.54. --- 6. **Problem b:** Umar took a loan of RM8,000 for 27 months and paid RM1,080 interest. Find the rate of interest. 7. Convert time to years: $$ t = \frac{27}{12} = 2.25 \text{ years}$$ 8. Use simple interest formula: $$ I = P \times r \times t $$ Given: - $I = 1080$ - $P = 8000$ - $t = 2.25$ 9. Solve for rate $r$: $$ r = \frac{I}{P \times t} = \frac{1080}{8000 \times 2.25} = \frac{1080}{18000} = 0.06 = 6\% $$ 10. **Answer:** The rate of interest is 6%.