Question

find the compound interest on 1500 for 9 months at the rate of 4 percent per annum, the interest being paid quarterly.​

Answer 1

Answer:

Given, P=125000,

As compounded quarterly R=

4

8

=2%

Time =9 months=

12

9

years =

12

9

×4quarters =3 quarters

We know, Amount =A=(1+

100

R

)

n

A=125000[

1+(

100

2

)

]

3

= Rs. 132651

C.I = Rs. [

132651−125000

]= Rs. 7651

Answer 2

Given:-

• Principal = Rs.1500
• Time = 9 months
• Rate = 4% p.a.

To find:-

• Compound interest is the interest is compounded quarterly.

Solution:-

We are given with time as 9 months which we need to convert into years.

Hence,

9 months = $\sf{\dfrac{9}{12} = \dfrac{3}{4}years}$

Now,

We know,

$\sf{A = P\bigg(1+\dfrac{r}{400}\bigg)^{4n}}$

Hence,

$\sf{A = 1500 \bigg(1 + \dfrac{4}{400}\bigg)^{4\times \dfrac{3}{4}}}$

= $\sf{A = 1500\bigg(1 + \dfrac{1}{100}\bigg)^3}$

= $\sf{A = 1500 \bigg(\dfrac{100+1}{100}\bigg)^3}$

= $\sf{A = 1500\bigg(\dfrac{101}{100}\bigg)^3}$

= $\sf{A = 1500\bigg(\dfrac{101}{100}\bigg)\bigg(\dfrac{101}{100}\bigg)\bigg(\dfrac{101}{100}\bigg)}$

= $\sf{A = \dfrac{156090601500}{100000000}}$

= $\sf{A = 1560.9}$

Now,

We know,

CI = Amount - Principal

Hence,

CI = 1560.9 - 1500

CI = 60.9

Therefore the interest after 9 months if the interest is compounded quarterly will be Rs.60.9.

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Explore More!!

The formula to find Amount when the interest is compounded annually:-

• $\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^n}$

The formula to find Amount when the interest is compounded half - yearly:-

• $\sf{A = P\bigg(1+\dfrac{r}{200}\bigg)^{2n}}$

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