Question

What is the principal amount which earns \[Rs.1320\] as compound interest for the second year at \[10%\] per annum.
1). \[Rs.10000\]
2). \[Rs.12000\]
3). \[Rs.13200\]
4). \[Rs.11880\]

Answer 1

Hint: In this question consider the amount for first year and second year be \[{{a}_{1}}\] and \[{{a}_{2}}\] and find out the value of \[{{a}_{1}}\] and \[{{a}_{2}}\] by applying the formula for amount and then find out the principal amount by subtracting the amount of first year from the amount of second year and check which option is correct in the given options.

Complete step-by-step solution:
The main distinction between simple and compound interest is that simple interest is calculated on the principal amount, whereas compound interest is calculated on the principal amount plus the interest compounded for a period cycle.
Simple interest and compound interest are two essential concepts that are commonly employed in various financial services, particularly in banking. Simple interest is used in loans such as instalment loans, auto loans, student loans, and mortgages. Compound interest is employed by the majority of savings accounts to pay interest. It pays a lot more than just interest. Let's take a closer look at the difference between simple and compound interest in this post.
Compound interest is interest earned on both the principal and the interest over a set period of time. The principal is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the next time period. Compound interest is a novel method of calculating interest that is utilised in all financial and economic operations worldwide. When we look at the compound interest values accumulated over successive time periods, we can see how powerful compounding is.
Now, according to the question:
We have given
\[C.I=Rs.1320\]
\[t=2year\]
Rate that is \[r=10%\] per annum
Let the amount at the end of first year be \[{{a}_{1}}\]
Therefore we will apply the formula\[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]
\[\Rightarrow {{a}_{1}}=P{{\left( 1+\dfrac{10}{100} \right)}^{1}}\]
\[\Rightarrow {{a}_{1}}=P{{\left( 1+\dfrac{1}{10} \right)}^{1}}\]
\[\Rightarrow {{a}_{1}}=P\left( \dfrac{11}{10} \right)\]
\[\Rightarrow {{a}_{1}}=(1.1)P\]
Let the amount at the end of second year be \[{{a}_{2}}\]
Therefore we will apply the formula \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]
\[\Rightarrow {{a}_{2}}=P{{\left( 1+\dfrac{10}{100} \right)}^{2}}\]
\[\Rightarrow {{a}_{2}}=P{{\left( 1+\dfrac{1}{10} \right)}^{2}}\]
\[\Rightarrow {{a}_{2}}=P{{\left( \dfrac{11}{10} \right)}^{2}}\]
\[\Rightarrow {{a}_{2}}={{(1.1)}^{^{2}}}P\]
\[\Rightarrow {{a}_{2}}=P(1.21)\]
Compound interest earned during the second year will be:
\[\Rightarrow C.I={{a}_{2}}-{{a}_{1}}\]
\[\Rightarrow 1320=P(1.21)-P(1.1)\]
\[\Rightarrow 1320=P(1.21-1.1)\]
\[\Rightarrow 1320=P(0.11)\]
\[\Rightarrow P=\dfrac{1320}{0.11}\]
\[\Rightarrow P=12000\]
Hence option \[(2)\] is correct.

Note: Simple interest is a fixed proportion of the principal amount borrowed or lent that is paid or received over a period of time. In the case of compound interest, interest is always higher than in the case of simple interest and the rate of formula is always given in fraction.