Sure, let's solve this step-by-step.
To find the simple interest and total amount after interest, we'll use the formula for simple interest and related steps:
Step 1: Understanding the Problem
- Principal amount ([tex]\(P\)[/tex]) = N5000
- Time ([tex]\(T\)[/tex]) = 3 months
- Annual interest rate ([tex]\( R \)[/tex]) = 5%
Step 2: Converting Months to Years
Since interest rates are usually given per annum (per year), we need to convert the time from months to years.
- [tex]\( T \)[/tex] in years = 3 months / 12 months/year = 0.25 years
Step 3: Applying the Simple Interest Formula
The formula for simple interest ([tex]\(SI\)[/tex]) is:
[tex]\[ SI = \frac{P \times R \times T}{100} \][/tex]
Substitute the known values into the formula:
- [tex]\( P = 5000 \)[/tex]
- [tex]\( R = 5 \)[/tex]
- [tex]\( T = 0.25 \)[/tex]
[tex]\[ SI = \frac{5000 \times 5 \times 0.25}{100} \][/tex]
Step 4: Calculating the Simple Interest
[tex]\[ SI = \frac{5000 \times 5 \times 0.25}{100} = \frac{6250}{100} = N62.5 \][/tex]
So, the simple interest is N62.5.
Step 5: Calculating the Total Amount
The total amount after interest ([tex]\(A\)[/tex]) is the sum of the principal and the simple interest:
[tex]\[ A = Principal + SI \][/tex]
[tex]\[ A = 5000 + 62.5 = N5062.5 \][/tex]
Conclusion
- The simple interest on N5000 in 3 months at the rate of 5% per annum is N62.5.
- The total amount after 3 months, including interest, is N5062.5.
So, the correct answer is that the total amount is N5062.5 and the simple interest is N62.5.
