Question

Marie invested K12000 in two different accounts at simple interest. The first one at 3% for 2 years and the second one for 3 years at 5.5%.
Find the Simple Interest

Answer 1

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**.