Question

Use the formula for compound amount to find the interest amount:$20,000 at 4% compounded quarterly for 3/4 of a year

Answer 1

Given

$20,000 at 4% compounded quarterly for 3/4 of a year

To find the interest amount.

Now,

The principal amount is $20,000, rate of interest r is 4% and time taken t is 3/4 of a year.

Then, the formula for amount compounded quarterly is given by,

$A=P(1+\frac{r}{100})^{4t}$

Then,

$\begin{gathered} A=20000(1+\frac{4}{100})^{4\times\frac{3}{4}} \\ =20000(1+\frac{1}{25})^3 \\ =20000(\frac{26}{25})^3 \\ =22497.28 \end{gathered}$

Hence, the amount is Rs. 22497.28.

Therefore, the compound interest is given by,

$\begin{gathered} CI=\text{Amount}-Prin\text{ciple} \\ =22497.28-20000 \\ =2497.28 \end{gathered}$

Hence, the compound interest is Rs. 2497.28.