Question

Example 5: Find the compound interest on 8,000 for six months at 20% per annum
compounded quarterly.
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Answer 1

Answer:

• compound interest = 7559

Given:

• principal = 8000

• Time = 6 months = 2 Quarterly

• Rate = 20% = 5% per Quarterly

To find:

• compound interest

Solution:

As we know that,

$\sf \implies {A = p(1 + \dfrac{r}{100})}$

where,

• p is principal (8000)

• r is rate ( 5% )

$\sf \implies{A = 8000(1 + \dfrac{5}{100})}$

$\sf \implies{A = 8000( \dfrac{105} {100})} {}^{2}$

$\sf \implies{A = 8000+ \dfrac{105}{100} \times \dfrac{105}{100}}$

$\sf \implies{A = 21 \times 21}$

$\sf \implies{A = 441}$

Now we have to find compound interest:

As we know that formula:

$\sf \implies{compound \: interest = A - P}$

where

• A is 441

• P is 8000

$\sf \implies{compound \: interest =441 - 8000 = }$

Hence, compound interest is 7559

Answer 2

Principal = 8000

rate = 20 % p.a.

time = 6 month = 2 time period

compounded quarterly

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A = 8000(1+5/100)²

# rate 5% is because when compounded quarterly, rate is divided by 4 ( 20/4 = 5 )

A = 8000(1+1/20)²

A = 8000(21/20)²

A = 8000 × 441/400

A = 20 × 441

A = 8820

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Compound interest = Amount - Principal

Compound interest = 8820 - 8000

Compound interest = 820