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A sum of ₹32,760 was taken as a loan. This is to be paid in three equal annual instalments. If the rate of interest is 20% compounded annually, then t
Question

A sum of ₹32,760 was taken as a loan. This is to be paid in three equal annual instalments. If the rate of interest is 20% compounded annually, then the value of each instalment is:

A.

₹11000

B.

₹10000

C.

₹15552

D.

₹16552​

Correct option is C

Given:

Amount taken as loan = ₹32,760

Instalment =3

Rate of interest = 20%

Formula Used:

In case of compound interest

Borrowed money =(x(1+r100)+x(1+r100)2+x(1+r100)3.) \left(\frac{x}{\left(1+\frac{r}{100}\right)}+\frac{x}{\left(1+\frac{r}{100}\right)^{2}}+\frac{x}{\left(1+\frac{r}{100}\right)^{3}} .…\right)​​

Solution:

Let the instalment be x

32760=(x(1+20100)+x(1+20100)2+x(1+20100)3)32760 =\left(\frac{x}{\left(1+\frac{20}{100}\right)}+\frac{x}{\left(1+\frac{20}{100}\right)^{2}}+\frac{x}{\left(1+\frac{20}{100}\right)^{3}}\right)​​

32760=(x(120100)+x(120100)2+x(120100)3)32760 =\left(\frac{x}{\left(\frac{120}{100}\right)}+\frac{x}{\left(\frac{120}{100}\right)^{2}}+\frac{x}{\left(\frac{120}{100}\right)^{3}}\right) ​​

32760=(5x6+25x36+125x216)32760 =\left(\frac{5x}{6}+\frac{25x}{36}+\frac{125x}{216}\right)​​

32760=(180x+150x+125x216)32760 =\left(\frac{180x+150x+125x}{216}\right)​​

32760=(455x216)32760 =\left(\frac{455x}{216}\right)​​

x=15,552x= ₹15,552​​

Alternative Method:

20%=20100=1520\% = \frac{20}{100} =\frac{1}{5}​​

5              6 × \times ​36

25          36  × \times​ 6

125      216

180        216  

150        216  

125        216

Total

455        216

455 is equivalent to principle and 216 is the instalment 

Now  455 = 32760

216=32760455×216=15,552216 = \frac{32760}{455} \times 216 = ₹15,552​​

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