Question

Calculate the amount and the compound interest on Rs 12000 in 2 years at \[5\% \] per annum compounded annually.
A) Rs 13500 and Rs 1500
B) Rs 13,230 and Rs 1230
C) Rs 14728 and Rs 2,728
D) None of the above

Answer 1

Hint:
Here we need to find the value of the amount and the compound interest. We will use the formula of amount to calculate the value of the required amount and then we will calculate the compound interest which will be equal to the difference of the value of the amount and the value of the principal amount. We will substitute the value of amount and the value of the principal amount to get the required value of the compound interest.

Formula Used:
We will use the following formulas:
1) If the amount is compounded annually, then the amount is given by \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}\] where \[A\] is the amount, \[P\]is the principal, \[R\] is the rate of Interest and \[t\] is the number of years.
2) Compound Interest is given by the formula \[C.I. = A - P\] where \[A\] is the amount, \[P\]is the principal.

Complete Step by Step Solution:
From the question, we get following data:
Principal amount \[\left( P \right) = {\rm{Rs}}12,000\]
Time \[\left( t \right) = 2{\rm{years}}\]
Rate of interest \[ = 5\% \]
Now, we will calculate the amount.
Substituting \[P = {\rm{Rs}}12,000\], \[t = 2{\rm{years}}\] and \[R = 5\] in the formula of the amount \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}\], we get
\[A = 12000 \times {\left( {1 + \dfrac{5}{{100}}} \right)^2}\]
On further simplifying the terms, we get
\[ \Rightarrow A = 12000 \times {\left( {1 + 0.05} \right)^2}\]
On adding the terms inside the bracket, we get
\[ \Rightarrow A = 12000 \times {\left( {1.05} \right)^2}\]
Now, we will apply the exponent on the base. Therefore, we get
\[ \Rightarrow A = 12000 \times 1.1025\]
On multiplying the terms, we get
\[ \Rightarrow A = {\rm{Rs}}13,230\]
Now, we will calculate the compound interest for the given principal.
Substituting \[P = {\rm{Rs}}12,000\] and \[A = {\rm{Rs}}13,230\] in the formula \[C.I. = A - P\], we get
\[C.I. = 13230 - 12000\]
On subtracting the numbers, we get
\[ \Rightarrow C.I. = {\rm{Rs}}1,230\]
Therefore, the value of amount and the value of compound interest are Rs 1,3230 and Rs 1,230.

Hence, the correct option is option B.

Note:
We might make a mistake by finding out simple interest instead of compound interest. The difference between simple interest and compound interest is that simple interest is based only on the principal amount remaining for every year. Whereas in compound interest, principal amount changes as the interest of every year is added to the principal amount and the compound interest is calculated on the increased principal amount.
While calculating compound interest, the number of compounding periods makes a significant difference. The higher the number of compounding periods, the greater will be the amount of compound interest.