To find the total simple interest earned from both investments, we can calculate the simple interest for each investment using the formula:
\[ \text{Simple Interest (SI)} = P \times r \times t \]
where:
- \( P \) is the principal amount (the initial investment),
- \( r \) is the rate of interest per period (as a decimal),
- \( t \) is the time the money is invested for (in years).
Calculation for the First Investment
Details:
- Principal (\( P_1 \)) = K12000
- Rate (\( r_1 \)) = 3% = 0.03
- Time (\( t_1 \)) = 2 years
\[ SI_1 = P_1 \times r_1 \times t_1 = 12000 \times 0.03 \times 2 \] \[ SI_1 = 12000 \times 0.03 = 360 \quad \text{(for 2 years)} \] \[ SI_1 = 360 \times 2 = 720 \]
Calculation for the Second Investment
Details:
- Principal (\( P_2 \)) = K12000 (we assume the total investment is split, since there's no further information on how much goes into each account, we can take \( P_2 \) as the remaining amount; however, since we are not provided with more details, we will just assume K12000 is invested in total)
- Rate (\( r_2 \)) = 5.5% = 0.055
- Time (\( t_2 \)) = 3 years
Assuming the second investment is also K12000, if she invested it all:
\[ SI_2 = P_2 \times r_2 \times t_2 = 12000 \times 0.055 \times 3 \] \[ SI_2 = 12000 \times 0.055 = 660 \quad \text{(for 3 years)} \] \[ SI_2 = 660 \times 3 = 1980 \]
Total Simple Interest
Now, we can sum the simple interests from both accounts:
\[ \text{Total SI} = SI_1 + SI_2 = 720 + 1980 = 2700 \]
Thus, the total simple interest earned from both accounts over the investment periods is K2700.