Question

Fabina borrows Rs.12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Answer 1

Concept :

It is the question asked in interest ones. Like as we know if we borrow money we borrow it on some percent of interest . Same thing is in this question .

Let's understand the question :

Here there are two girl Fabina and Radha both borrow same amount of money at 10% of interest which is compounded annually.

It is asked who pays more interest ? And if anyone by how much ?

Solution :

Let fabina pays x amount of interest and radha pays y amount of interest .

Now , we will see the amount paid by both after 3 years.

For finding amount paid by Fabina -

P = Rs. 12,500

N = 3 years.

R = 12%

$∴ \: SI = \frac{P×R×N}{100}$

$= Rs \frac{12500 \times 3 \times 12}{100}$

$= Rs \: 125 \times 3 \times 12 \\ = Rs \: 4500$

For finding amount paid by Radha -

P = Rs. 12500

N = 3 years.

R = 10% which is compounded annually.

$a = \: p(1 + \frac{r}{100} ) {}^{n}$

$= Rs \: 12500(1 + \frac{10}{100} ) {}^{3}$

$= Rs \: 12500( \frac{11}{10} ) {}^{3}$

$= Rs \: 12500 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10}$

$= Rs \frac{125 \times 11 \times 11 \times 11}{10}$

$= Rs \:16637.5$

∴ CI = Rs. 16637.5 - 12500= Rs. 4137. 50

Therefore , amount paid by radha = Rs. 4137.50

So , difference of money = Rs. 4500 - Rs. 4137.50

= Rs. 362.5

• Therefore, Fabina pays Rs. 362.5 more.

Answer 2

$\huge \rm \fbox {\underline{required \: answer}}$

Fabina.

Principal → ₹12,500

Rate of interest = ₹12% P.A

Time = 3 years

$\large \rm{simple \: interest = \frac{P × R × T }{100}}$

$\large : \longrightarrow {\frac{12500 \times 12 \times 3}{100}}$

$\large \fbox{ = 4500}$

Radha.

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

$: \longrightarrow{(1 + \frac{10}{100}} )^{3} = 12500 \: ( \frac{10 + 1}{10})^{3}$

$\rm{ = 12500 \: ( \frac{11}{10} \times \frac{11}{10} \times \times \frac{11}{10}} )$

$\rm \large{ \frac { = 166375}{10}} = 16637.5$

$\large \rm{[I = A-P = 4137.5 ]}$

Interest paid by fabina = ₹4500

Interest paid by radha = 4137.5

$\rm{fabina \: paid \: more \: interest \: than \: radha.}$

$\rm{ = 4500 - 4137.5}$

$\rm{ = 362.5}$

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