Calculate the amount and compound interest for Rs.20000 for 3 years at 8% per annum compounded annually.
ANSWER
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Hint: We can easily solve this question using the formula \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}\], where A denotes the final amount, P denotes the principle amount provided to us, R is the rate of interest on which we have to calculate the compound interest and t denotes the time for which the amount is kept for compound interest.
Complete step-by-step solution -
Given that Rs.20000 for 3 years at 8% per annum compounded annually, we have to calculate the amount and the Compound interest. Values of the above variables are as given below, Principal P = Rs 20000 Rate of interest R = 8% per annum Time duration t = 3 years We have to calculate Amount and Compound interest CI by using the formula, \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}\], where A denotes the final amount, P denotes the principle amount provided to us, R is the rate of interest on which we have to calculate the compound interest and t denotes the time for which the amount is kept for compound interest.
Now we substitute the values in the formula: \[\begin{align} & A=20000{{\left( 1+\dfrac{8}{100} \right)}^{3}} \\ & \Rightarrow A=20000{{\left( 1+\dfrac{2}{25} \right)}^{3}} \\ & \Rightarrow A=20000{{\left( \dfrac{27}{25} \right)}^{3}} \\ & \Rightarrow A=20000{{\left( 1.08 \right)}^{3}} \\ & \Rightarrow A=20000\left( 1.25 \right) \\ & \Rightarrow A=25000 \\ \end{align}\] Now the final amount after adding the principle and the compound interest is given by, Amount A = Rs 25000 We now proceed to calculate the compound interest. Therefore, the compound interest will be CI = A – P CI = 25000 – 20000 CI = Rs.5000 So, the answer of the question is: Amount A = Rs. 25000 Compound Interest CI = Rs. 5000
Note: The possibility of error in these types of questions can be at the point where you have to calculate the Compound interest after calculating the Amount. Always apply the right formula and the right substitutions to get the correct solution.