Question

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3. Fabina borrows ₹ 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?
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Answer 1

Answer:

Question :-

• Fabina borrows ₹ 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?

Given :-

• Fabina borrows ₹ 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.

Find Out :-

• Who pays more interest and 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%

✭ $\bf SI = \dfrac{P×R×N}{100}$ ✭

➙ $\sf SI =\: \dfrac{12500 \times 3 \times 12}{100}$

➙ $\sf SI = \: 125 \times 3 \times 12$

$\implies$ ${\small{\bold{\purple{\underline{SI =\: Rs \: 4500}}}}}$

For finding amount paid by Radha -

• P = Rs. 12500
• N = 3 years.
• R = 10% which is compounded annually.

✭ $\bf A = \: P\bigg(1 + \dfrac{r}{100} \bigg)^{n}$ ✭

➙ $\sf A = \: 12500\bigg(1 + \dfrac{10}{100} \bigg) {}^{3}$

➙ $\sf A = \: 12500\bigg( \dfrac{11}{10} \bigg) {}^{3}$

➙ $\sf A = \: 12500 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10}$

➙ $\sf A = \dfrac{125 \times 11 \times 11 \times 11}{10}$

$\implies$ ${\small{\bold{\purple{\underline{A =\: Rs \: 16637.5}}}}}$

∴ 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

Henceforth, Fabina pays Rs. 362.5 more.

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Answer 2

For Fabina

principle = Rs.12500

rate of interest = 12% p.a

time = 3 years

S.I = P x R x T / 100

Rs. (12500×12×13/100) = Rs. 4500

so the interest is Rs.4500

For Radhika

Amount = P(1+R/100) to the power t

Amount = Rs. [1250 × (1+10/100) to the power 3

Amount = Rs. (12500 × 110/100 × 110/100 × 110×100)

Amount = Rs. 16637.50

Simple interest = (16377.50 - 12500)

Simple interst = 4137.50

so fabina pays more by 362.50

we will simply subtract both fabina and radhika si to find out who pays more and how

fabina si = 4500

radhika si = 4137.50

so the difference is 362.50

final answer

fabina pays more by 362.50