Question

The compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is:
a) 1260
b) 1261
c) 1271
d) 1281

Answer 1

Hint: Use the formula of compound interest $C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$, where P is the principal (or original amount), r is the annual rate, n is the number of times interest compounded per time period, t is the number of years on which interest has applied.

Complete step-by-step answer:

We are going to use the formula of compound interest which is written below:

$C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$

Where P: the Principal (or original amount)

r: annual rate of interest

n: number of times interest compounded per time period

t: number of years on which the interest has applied

It is given that:

The principal (or original amount) is Rs 8000.

Annual rate of interest is 20%.

The interest is compounding quarterly means n = 4.

The interest compounded quarterly for 9 months means $t=\dfrac{9}{12}$year.

Now, substituting these values in the compound interest formula we get,

$\begin{align}

  & C.I.=8000{{\left( 1+\dfrac{20}{100\left( 4 \right)} \right)}^{4\times \dfrac{9}{12}}}-8000 \\

 & C.I.=8000{{\left( 1+(0.25\times 0.2) \right)}^{3}}-8000 \\

 & C.I.=8000{{\left( 1+.05 \right)}^{3}}-8000 \\

 & C.I.=9261-8000 \\

 & C.I.=1261 \\

\end{align}$

So, the compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is 1261.

Hence, the correct option is (b).

Note: While applying the formula of compound interest there are some common mistakes that could happen:
When substituting the value of r, don’t forget to divide the rate by 100.
There could be confusion with the “compounded quarterly” statement, it means in a year interest is 4 times compounded so n value will be 4.
And the “t” should be in years if in the question “t” is not given in years first convert it into years then apply in the formula.