Question

Find the compound interest on Rs 160000 for one year at the rate of 20% per annum, if
the interest is compounded quarterly.​

Answer 1

Answer :

• The compound interest on Rs 160000 for one year at the rate of 20% per annum (compounded qquarterly) is Rs. 34481.

Explanation :

Given :

• Principal = Rs. 160000
• Rate of interest = 20 %
• Time period = 1 year

To find :

• Compound interest

Knowledge required :

• Formula for Compound Interest (Compounded Quarterly) :

⠀⠀⠀⠀⠀⠀⠀⠀⠀CI = P[(1 + R/4/100)^4n - 1]

Where :

• CI = Compound Interest
• R = Rate of interest
• n = Time period
• P = Principal

Solution :

By using the formula Compound Interest and substituting the values in it, we get :

==> CI = P[(1 + R/4/100)^4n - 1]

==> CI = 160000(1 + 20/4/100)⁴ - 1]

==> CI = 160000[(1 + 5/100)⁴ - 1]

==> CI = 16000[{(100 + 5)/100}⁴ - 1]

==> CI = 160000[(105/100)⁴ - 1]

==> CI = 160000[(21/20)⁴ - 1]

==> CI = 160000 × (194481/160000 - 1)

==> CI = 160000 × (194481 - 160000)/160000

==> CI = 160000 × 34481/160000

==> CI = 34481

∴ CI = Rs. 34481

Hence the Compound Interest is Rs. 34481.

Answer 2

$\sf{\bold{\pink{\underline{\underline{Given :}}}}}$

Principle = Rs. 1,60,000

Rate = 20%

Time = 1 year

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$\sf{\bold{\green{\underline{\underline{To\:Find :}}}}}$

Compound Interest

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$\sf{\bold{\red{\underline{\underline{Solution :}}}}}$

$\sf{\blue{\boxed{\bold{Amount = P \bigg\lgroup 1 +\dfrac { \dfrac{rate}{4}}{100}\bigg\rgroup^{4n}-1}}}}$

$\sf :\implies\: {\bold{ CI = 160000 \bigg\lgroup 1 + \frac {\dfrac{20}{4}}{100}\bigg\rgroup^{4}-1 }}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup 1+ \dfrac{5}{100}\bigg \rgroup^4-1}}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup \dfrac{105}{100}\bigg \rgroup^4-1}}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup \dfrac{21}{20}\bigg \rgroup^4-1}}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup \dfrac{194481}{160000}\bigg \rgroup-1}}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup \dfrac{194481 - 160000}{160000}\bigg \rgroup}}$

$\sf :\implies\: {\bold{ CI = 160000\times\bigg \lgroup \dfrac{34481}{160000}\bigg \rgroup}}$

${\boxed{ \sf\: {\bold{CI = 34481}}}}$