Problems Where the Interest is not Compounded

We know how to find the compound interest using the following formula:

Amount,

Here, P is the principal, R is the rate of interest per annum, and n is the number of years.

Let us now try to solve an example.

What is the amount received after years when Rs 20000 are invested at the rate of 6% p.a. compounded half yearly?

Do you find any difference between this question and the questions you have solved before?

Yes, in this example, the interest is compounded half yearly. In the questions we have solved before, the interest was compounded annually.

The time interval after which the interest is compounded is known as the conversion period.

In the given example, the conversion period is six months as the interest is compounded half yearly.

To solve such questions where the interest is not compounded annually, we have to change the rate and time accordingly.

In the given example, the time period is given asyears.

Here, the conversion period is six months.

Number of conversion periods = 3

Rate of interest = 6% per annum

= 3% per half yearly

Now, we can solve this question using the same formula.



Where,

n is the number of conversion periods and R is the rate per conversion period.



Hence, the amount received after years is Rs 21854.54.

Before solving more examples, let us see the following table that will help us find the number of conversion periods and the rate of interest per conversion period.

Let R be the rate of interest per annum and t be the number of years.

Then,

When the interest is compounded
Number of conversion periods (n)
Rate of interest per conversion period (r)

Half yearly
t × 2


Quarterly
t × 4


Monthly
t × 12



Now, let us solve some more examples.

Example 1:

The compound interest on a certain sum invested for one year at the rate of 10% per annum compounded half yearly is Rs 5125. Find the sum.

Solution:

Let P be the sum.

Compound interest = Rs 5125

Amount, A = P + 5125

Number of conversion periods, n = 1 × 2 = 2

Rate of interest per conversion period

We know that,



Hence, the sum is Rs 50000.

Example 2:

Lalit borrowed Rs 125000 from his friend at the rate of 8% per annum compounded quarterly. After some time, he re-paid Rs 132651 to his friend. For how long did Lalit borrow the money?

Solution:

Principal, P = Rs 125000

Amount, A = Rs 132651

Let n be the number of conversion periods.

Rate of interest per conversion period,

We know that,



\ Number of conversion periods = 3

Here, the interest is compounded quarterly.



Hence, Lalit borrowed the money for a period of 9 months.