Question

Find the compound interest on 5000 for 3 years at 6% per annum.

Answer 1

Hint: In this particular question use the concept that the compound interest is calculated as, $$C.I.=A-P$$, where P = Principle amount and A = Amount after compound interest. So, A is calculated as $$A=P{(1+{\displaystyle \frac{r}{100}})}^n$$, where r is the rate of interest in percentage, n is the time in years. So, use these concepts to reach the solution of the equation.

Complete step by step answer:
Given data: principle amount = 5000 Rs.
Rate of interest = 8% per annum
‘n’ time in years = 3 years
Now, we know that the compound interest is calculated as $$C.I.=A-P$$ and here $$A=P{(1+{\displaystyle \frac{r}{100}})}^n$$.
So, $$A=5000\times {(1+{\displaystyle \frac{6}{100}})}^3$$
Now, we see that the power is not in fraction, so we will not convert this power into integer by multiplying by 2, for this we have to divide the rate of interest by 2, so that overall no change i.e., $$n=3$$ years and $$r=6\mathrm{\%}$$ p.a.
So, he got 6% interest per annum for 3 years. Compounded monthly, is the same as he got at 6% interest per annum for 3 years.
Compounded annually.
$$\begin{array}{rl}& \Rightarrow A=5000{(1+{\displaystyle \frac{6}{100}})}^3\\ & \Rightarrow A=5000{\left({\displaystyle \frac{106}{100}}\right)}^3\\ & \Rightarrow A=5000{\left({\displaystyle \frac{53}{50}}\right)}^3=5000\times {\displaystyle \frac{53}{50}}\times {\displaystyle \frac{53}{50}}\times {\displaystyle \frac{53}{50}}\\ & \Rightarrow A=5955.08\end{array}$$
Amount $$=5955.08$$
So, $$C.I.=A-P=5955.08-5000$$
$$C.I.=955.08$$
Therefore, compound interest is 955.08.

Note: Whenever we face such types of questions the key concept we have to remember is the formula of compound interest which is stated above. So, first change the given compounded monthly to compounded yearly. Then convert to fraction in integer by multiplying it by 12 and divide the interest by the same number. So, overall no change will occur.