To solve this problem, we need to calculate both the simple interest accrued over five years and the total amount the farmer will need to pay back at the end of that period.
### Step-by-Step Solution:
1. Identify the given values:
- Principal (P): #1,600.00
- Annual interest rate (R): 2.5% per annum
- Time (T): 5 years
2. Convert the interest rate from a percentage to a decimal:
- Convert 2.5% to a decimal by dividing by 100:
[tex]\[
R = \frac{2.5}{100} = 0.025
\][/tex]
3. Calculate the simple interest using the formula:
[tex]\[
\text{Simple Interest} = P \times R \times T
\][/tex]
Substitute the given values into the formula:
[tex]\[
\text{Simple Interest} = 1600 \times 0.025 \times 5
\][/tex]
4. Perform the multiplication to find the simple interest:
[tex]\[
\text{Simple Interest} = 1600 \times 0.025 = 40
\][/tex]
[tex]\[
\text{Simple Interest} = 40 \times 5 = 200
\][/tex]
So, the simple interest accrued over five years is #200.00.
5. Calculate the total amount to be paid back:
[tex]\[
\text{Total Payment} = \text{Principal} + \text{Simple Interest}
\][/tex]
Substitute the values we have:
[tex]\[
\text{Total Payment} = 1600 + 200
\][/tex]
6. Perform the addition to find the total payment:
[tex]\[
\text{Total Payment} = 1800
\][/tex]
### Conclusion:
At the end of five years, the farmer will have to pay back #200.00 in interest, making the total amount he needs to pay back to the bank #1,800.00.
