Certainly! Let's solve this problem step-by-step.
We have the following information given:
- Principal amount ([tex]\( P \)[/tex]) = ₹ 5675
- Annual interest rate ([tex]\( R \)[/tex]) = 8.5%
- Time period ([tex]\( T \)[/tex]) = [tex]\( 4 \frac{1}{3} \)[/tex] years
Firstly, we convert the time period given in mixed fraction to an improper fraction for easier calculation:
[tex]\[ T = 4 + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{13}{3} \text{ years} \][/tex]
Now we can use the simple interest formula to calculate the interest accrued over the time period:
[tex]\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \][/tex]
Substitute the values into the formula:
[tex]\[ SI = \frac{5675 \times 8.5 \times \frac{13}{3}}{100} \][/tex]
Now, calculate the product:
[tex]\[ 5675 \times 8.5 = 48237.5 \][/tex]
Multiply this result by [tex]\( \frac{13}{3} \)[/tex]:
[tex]\[ \text{Numerator} = 48237.5 \times 13 = 627087.5 \][/tex]
Divide this by 3:
[tex]\[ \frac{627087.5}{3} = 209029.16666666666\][/tex]
And finally, divide by 100 to find the interest:
[tex]\[ SI = \frac{209029.16666666666}{100} = 2090.2916666666665 \][/tex]
Thus, the simple interest accrued over [tex]\(4 \frac{1}{3}\)[/tex] years is:
[tex]\[ \text{Simple Interest} = ₹ 2090.29 \][/tex]
Next, to find the total amount to be paid at the end of the period, we add the simple interest to the principal amount:
[tex]\[ \text{Total Amount} = P + SI \][/tex]
Substitute the values:
[tex]\[ \text{Total Amount} = 5675 + 2090.29 = 7765.29 \][/tex]
Therefore, the amount to be paid at the end of [tex]\( \)[/tex] years at a rate of 8.5% on a principal of ₹ 5675 is:
[tex]\[ \text{Amount to be Paid} = ₹ 7765.29 \][/tex]
