Question

When the interest is compounded quarterly, there are four conversion periods in a year and the quarterly rate will be
A. one-third of the annual rate
B. one-fourth of the annual rate
C. three-fourth of the annual rate
D. two times the annual rate

Answer 1

Hint: First we recall the generalized formula for calculating the compound interest then, we will learn how to calculate the compound interest when interest is compounded quarterly (i.e. four times in a year).

Complete step-by-step answer:
We know that the general formula to calculate the compound interest is
Compound interest = Amount – Principal
And \[\text{Amount =}P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
Where, $ P= $ Principal
\[R=\] Rate of interest
 $ T= $ Time period
If the rate of interest is annual and the interest compounded quarterly (i.e. four times in a year) then the time period will be four times the actual time and the rate of annual interest will be one fourth of the actual annual rate. In this case we use the following formula to calculate the amount and compound interest-
\[A=P{{\left( 1+\dfrac{\dfrac{r}{4}}{100} \right)}^{4T}}\] and CI = Amount - Principal
So, when the interest is compounded quarterly, there are four conversion periods in a year and the quarterly rate will be one-fourth of the annual rate. Option B is the correct answer.

Note: Students must read question carefully about the compounding frequency i.e. interest compounded yearly, half-yearly, quarterly, monthly or weekly. Here for this question rate percent is divided by 4 and the time period (number of years) is multiplied by 4.