# When the interest is compounded half yearly, the number of conversion periods in a year is four. Is the following statement true or false

**Solution:**

The given statement is False.

When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.

The formula for the finding the amount at the end of a given period is given by:

Amount at the end of the period = Principal(1 + r/100)^{n}

r = rate of interest

n = conversion period

If r = annual rate of interest compounded annually and

n = number of years.

If the interest is compounded semi-annually (six monthly) then

Applicable rate of interest = r/2

Conversion period = 2n

The formula gets modified as:

Amount at the end of the period = Principal(1 + (r/2) x 100)^{2n}

**✦ ****Try this**: If the interest is compounded quarterly the conversion period will be 4 in a year. The given statement is True.

The applicable rate of interest in this case is r/4 (r = annual rate of interest).

Amount at the end of the period = Principal(1 + (r/4)100)^{n}

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 8

**NCERT Exemplar Class 8 Maths Chapter 9 Sample Problem 8**

## When the interest is compounded half yearly, the number of conversion periods in a year is four. Is the following statement true or false

**Summary:**

The statement is false. When the interest is compounded half yearly, the number of conversion periods in a year is four

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