Question

In what time will a sum of rupees 3750 at 20% per annum compounded annually amount to rupees 6480?​

Answer 1

P=3750

R=20%

Amt=6480

T=?

Amt=P[I+R/100]^n

6480=3750[1+20/100]^n

6480=3750[1+1/5]^n

6480=3750[6/5]^n

6480/3750=[6/5]^n

216/125=[6/5]^n

[6/5]^3=[6/5]^n

( when the bases are same powers

are also same)

so,[6/5]^3=[6/5]^3

Time=3 years

Hope It will help you

Answer 2

SOLUTION:-

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Given:

• Principal,[P]= Rs.3750
• Amount,[A]= Rs.6480
• Rate,[R]= 20% p.a.

To find:

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The time of the compound annually.

Explanation:

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We know that, formula of the compound Interest:

C.I.= Amount - Principal

&

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

According to the question:

$6480 = 3750(1 + \frac{20}{100} ) {}^{n} \\ \\ \frac{6480}{3750} = (1 + \frac{2}{10} ) {}^{n} \\ \\ \frac{648}{ 375} = ( \frac{10 + 2}{10} ) {}^{n} \\ \\ \frac{216}{125} = ( \frac{12}{ 10} ) {}^{n} \\ \\ \frac{216}{125} = ( \frac{6}{5} ) {}^{n} \\ \\ ( \frac{6}{5} ) {}^{3} = ( \frac{6}{5} ) {}^{n} \\ \\ n = 3 \: years$

Thus,

The time,[n] is 3 years.

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