To find the compound interest on ₹31,250 at an annual interest rate of 8% for 2 years and 3/4 of a year (which is 2.75 years), we can follow these steps:
### Step 1: Understand the formula for compound interest
Compound interest can be calculated using the formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money)
- [tex]\( r \)[/tex] is the annual nominal interest rate (as a decimal)
- [tex]\( n \)[/tex] is the number of times the interest is compounding per year
- [tex]\( t \)[/tex] is the time the money is invested for, in years
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( n \)[/tex] years, including interest
Since the interest is compounded annually in this case, [tex]\( n = 1 \)[/tex].
### Step 2: Substitute the given values into the formula
Here, the principal amount ([tex]\( P \)[/tex]) is ₹31,250, the annual interest rate ([tex]\( r \)[/tex]) is 8% or 0.08 as a decimal, and the time period ([tex]\( t \)[/tex]) is 2.75 years. Since the interest is compounded once per year ([tex]\( n = 1 \)[/tex]):
[tex]\[ A = 31250 \left(1 + \frac{0.08}{1}\right)^{1 \cdot 2.75} \][/tex]
### Step 3: Calculate the amount accumulated
[tex]\[ A = 31250 \left(1 + 0.08\right)^{2.75} \][/tex]
[tex]\[ A = 31250 \left(1.08\right)^{2.75} \][/tex]
Using the given numerical result:
[tex]\[ A \approx 38615.83 \][/tex]
### Step 4: Find the compound interest
Compound interest is the amount accumulated ([tex]\( A \)[/tex]) minus the principal ([tex]\( P \)[/tex]):
[tex]\[ \text{Compound Interest} = A - P \][/tex]
[tex]\[ \text{Compound Interest} = 38615.83 - 31250 \][/tex]
[tex]\[ \text{Compound Interest} \approx 7365.83 \][/tex]
### Final Answer:
- The amount accumulated after 2.75 years is approximately ₹38,615.83.
- The compound interest earned on ₹31,250 at an 8% interest rate per annum over 2.75 years is approximately ₹7,365.83.
