Question

find out the compound interest on 16000 for one year at 20% per annum when the interest is payable quarterly​

Answer 1

20 percent per year

if it will pays quarterly then rate =5%

time =3%

20 21

20 21

20 21

8000 9261

8000=16000

1=2000

then diff between P and A is 1261

1261=1261 ×2000

=2522000

Answer 2

Solution:

Principal = ₹16000

Rate = 20% p.a.

Time = 1year

$\tt{A =P\bigg\{1 + \dfrac{R}{400}\bigg\}^{4n}}$

$\sf{ = 16000 \bigg \{1 + \dfrac{20}{400} \bigg \}^{4 \times 1} }$

$\sf{ = 16000 \bigg \{1 + \dfrac{1}{20} \bigg \}^{4} }$

$\sf{ = 16000 \bigg\{ \dfrac{21}{20} \bigg \}^{4} }$

$\sf{ = 16000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}}$

$\sf{=16000\times\frac{194481} {160000} }$

$\sf = \cancel{\frac{194481}{10}}$

$\sf{ =₹19448.1}$

C.I = Final Amount - Original Principal

C.I = ₹19448.1 - ₹16000

C.I = ₹3448.1

$\therefore\tt{Compound \: Interest \: =₹3,448.1}$

$\rule{200pt}{1pt}$

Additional Information

When Interest is compounded annually

$\sf{A = P\bigg(1 + \frac{R}{100}\bigg)^n}$

When Interest is compounded half yearly

$\sf{A = P\bigg(1+ \frac{R}{200}\bigg)^{2n}}$

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