At the end of every even month we invest K175 into an account that bears interest of 11% p.a. compounded monthly. At the end of every odd month we invest K155. How much will be in the account at the end of 3 years?

To calculate the amount that will be in the account at the end of 3 years, we need to take into account the following details:

- The interest rate is 11% per annum, compounded monthly.
- Every **even month**: K175 is invested.
- Every **odd month**: K155 is invested.
- The total time period is 3 years, which is 36 months.

### Step-by-step calculation:

#### 1. Monthly interest rate:
The monthly interest rate is given by:
\[
i = \frac{11\%}{12} = \frac{11}{100 \times 12} = 0.009167 \text{ or } 0.9167\%
\]

#### 2. Amount at the end of 36 months:
We'll treat each set of investments (odd and even months) separately and sum the contributions at the end of the 36 months.

**Even months (K175 investment)**:
- The investment happens at the end of every even month (months 2, 4, 6, ..., 36).
- There are 18 even months in total.

The future value of an investment made \( n \) months before the end is calculated using the compound interest formula:
\[
FV = P(1 + i)^n
\]
where \( P \) is the amount invested, \( i \) is the monthly interest rate, and \( n \) is the number of months before the end.

For even months, the total future value can be calculated by summing up the contributions:

\[
FV_{\text{even}} = 175 \times (1+i)^{34} + 175 \times (1+i)^{32} + \dots + 175 \times (1+i)^0
\]

**Odd months (K155 investment)**:
- The investment happens at the end of every odd month (months 1, 3, 5, ..., 35).
- There are 18 odd months in total.

The future value for odd months is similarly calculated:

\[
FV_{\text{odd}} = 155 \times (1+i)^{35} + 155 \times (1+i)^{33} + \dots + 155 \times (1+i)^1
\]

#### 3. Total future value:
The total amount in the account at the end of 36 months is the sum of the future values for both even and odd months:
\[
FV_{\text{total}} = FV_{\text{even}} + FV_{\text{odd}}
\]

Now, I'll compute the total future value.The total amount in the account at the end of 3 years (36 months) will be approximately **K6997.88**.

Would you like more details or have any questions on how this was calculated?

Here are some related questions to deepen your understanding:

1. How would the result change if the interest were compounded quarterly instead of monthly?
2. What if the monthly investment amounts were the same for both odd and even months?
3. How would you calculate the total interest earned over the 3 years?
4. What would happen if the interest rate were variable each year?
5. How would the final amount change if no investments were made after the first year?

**Tip:** When dealing with compounded interest, always check the compounding frequency (monthly, quarterly, yearly), as it significantly affects the final amount.

Find out how much will be in an account after investing K175 at the end of every even month and K155 at the end of every odd month for 3 years with an interest rate of 11% p.a. compounded monthly. This problem involves compound interest calculations and is suitable for students in Grades 10-12.

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