find the compound interest and the total amount after 4 years and 6 months if the interest is compounded…

Explanation:

Step1: Convert time to years

4 years and 6 months = 4.5 years.

Step2: Use compound - interest formula for 4 years

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal, $r$ is the rate of interest per annum, and $n$ is the number of years. For $n = 4$ years, $P=\text{₹}100000$, and $r=\frac{10}{100}=0.1$. $A_4=100000\times(1 + 0.1)^4=100000\times1.1^4=100000\times1.4641=\text{₹}146410$.

Step3: Calculate simple interest for the remaining half - year

The simple - interest formula for the remaining half - year on the amount after 4 years is $I=\text{PRT}$, where $P = 146410$, $R = 10%=0.1$, and $T=\frac{1}{2}$ year. $I = 146410\times0.1\times\frac{1}{2}=\text{₹}7320.5$.

Step4: Calculate the total amount

The total amount $A$ after 4 years and 6 months is $A=A_4 + I$. $A=146410+7320.5=\text{₹}153730.5$.

Step5: Calculate the compound interest

Compound interest $CI=A - P$. $CI = 153730.5-100000=\text{₹}53730.5$.

Answer:

Total amount = ₹153730.5 Compound interest = ₹53730.5