solution

Solution to Question 8: Compound Interest

Given:

• Principal, \(P = ₹1,60,000\)
• Rate of interest, \(R = 10%\) per annum
• Time, \(T = 2\) years
• Interest is compounded half-yearly.

Step 1: Calculate the rate and number of periods

Rate per half-year:

\[ \frac{10}{2}=5% \]

Number of half-years:

\[ n=2\times 2=4 \]

Step 2: Calculate the amount

Using the compound amount formula:

\[ A=P\left(1+\frac{R}{100}\right)^n \]

Substituting the values:

\[ A=160000\left(1+\frac{5}{100}\right)^4 \]

\[ A=160000\left(\frac{105}{100}\right)^4 \]

\[ A=160000\times\frac{121550625}{100000000} \]

\[ \boxed{A=₹1,94,481} \]

Step 3: Calculate the compound interest

\[ \text{Compound Interest}=A-P \]

\[ =194481-160000 \]

\[ \boxed{\text{Compound Interest}=₹34,481} \]

Final Answer

Amount = ₹1,94,481

Compound Interest = ₹34,481