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+(r)/(100))^(4t)`

Then,

`\begin{gathered} A=20000(1+(4)/(100))^{4*(3)/(4)} \\ =20000(1+(1)/(25))^3 \\ =20000((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.