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# For calculation of interest compounded half yearly, keeping the principal same, which one of the following is true

(a) Double the given annual rate and half the given number of years

(b) Double the given annual rate as well as the given number of years

(c) Half the given annual rate as well as the given number of years

(d) Half the given annual rate and double the given number of years

**Solution:**

The answer is (d) i.e. half the given rate annual rate and double the given number of years.

If the rate of interest is 12% per annum, but is compounded half yearly then the effective or applicable rate of interest is :

r = 12%/2 = 6%

Since the interest is compounded half yearly the conversion period is 2 because there are two half yearly periods in one year. Therefore,

A = P(1 + 6/100)^{2}

= P(1.06)^{2}

**✦ ****Try This**: For calculation of interest compounded quarterly for one year , keeping the principal same, which one of the following is true.

(a) Divide the given annual rate by 4 and multiply the given number of year(s) by 4.

(b) Multiply the given annual rate by 4 as well as the multiply given number of year(s) by 4

(c) Divide the given annual rate by 4 as well divide the given number of years by 4

(d) Divide the given annual rate by 4 and multiply the given number of years by 4

Since the interest has to be calculated for two years and it is compounded half yearly, it implies that:

- The applicable or effective rate of interest will be divided by 4 i.e. r/4
- One year will be considered as 4 because the interest is compounded quarterly

If the rate of interest is 12% per annum, but is compounded quarterly then the effective or applicable rate of interest is :

r = 12%/4 = 3%

Since the interest is compounded quarterly the conversion period is 4 because there are two half yearly periods in one year. Therefore,

A = P(1 + 3/100)^{4}

= P(1.03)^{4}

Where P = principal

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

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

## For calculation of interest compounded half yearly, keeping the principal same, which one of the following is true (a) Double the given annual rate and half the given number of years, (b) Double the given annual rate as well as the given number of years, (c) Half the given annual rate as well as the given number of years, (d) Half the given annual rate and double the given number of years

**Summary:**

For calculation of interest compounded half yearly, keeping the principal same, then one half the given annual rate and double the given number of years

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