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? in steps please.

Answer 1

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.

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Find:

• Who pays more interest and by how much?

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Using formula:

• S.I = (Principal × Rate × Time)/100
• A = Principal (1 + Rate/100)ⁿ
• C.I = Amount - Principal

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Note:

• (ⁿ) = Number of years or Time period.

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Calculations:

• Finding for Radha:

= (12500 × 12 × 3)/100

= 450000/100

= 4500

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• Finding for Fabina:

= 12500 × (1 + 10/100)³

= 12500 × (11/10)³

= {12500 (11 × 11 × 11)}/1000

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= 125 × 1331/10

= 166375/10

= 16637.5

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Amount paid by Radha:

= 16637.50 - 12500

= 4137.5

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Fabia pays more:

= 4500 - 4137.50

= 362.5

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Hence, Fabia pays more 362.5 than Radha.

Answer 2

AnswEr :

• Fabina pays more interest with Rs 362.5 more .

Step-by-step explanation :

GivEn :

• 1st case (Fabina)

• Principal (P) = Rs 12500

• Rate of interest (R) = 12% Per annum.

• Time period (n) = 3 years

• 2nd case (Radha)

• Principal (P) = Rs 12500 [same amount]

• Rate of interest (R) = 10% Per annum.

• Time period (n) = 3 years

To find :

• Who pays more interest and by how much = ?

SoluTion :

Before directly calculating the compound interest, we'll calculate the simple interest at 12% rate for 3 years.

Interest paid by Radha :

$\implies$ 3 × 12500 × 12 / 100

$\implies$ 450000 / 100

$\implies$ Rs 4500 [ Radha's interest rate ]

Now,

we'll find out the total amount,

$\sf\implies \: \: \: A = P { \bigg( 1 + \dfrac{R}{100} \bigg) }^{n}$

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

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

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

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

$\sf\implies \: \: \: A = 12500 { \bigg(\dfrac{121 \times 11}{10 \times 10 \times 10} \bigg) }$

$\sf\implies \: \: \: A = { \bigg(\dfrac{125 \times 1331}{10 } \bigg) }$

$\sf\implies \: \: \: A = { \bigg(\dfrac{166375}{10 } \bigg) }$

$\sf\implies \: \: \: { \boxed{ \sf{A = 16637.5}}} \: \bigstar$

Also, we know that,

• A = P + I

where,

• A is amount

• P is principal

• I is interest rate

$\implies$ A = P + I

$\implies$ 16637.5 = 12500 + I

$\implies$ 16637.5 - 12500 = I

$\implies$ I = 4137.5 [ Fabina's interest rate ]

Here, we can clearly observe that interest rate paid by Fabina is more than that of Radha as,

[4500 > 4137.5 ]

Fabina pays more interest rate that of the Radha by :

$\implies$ Interest paid by Fabina - Interest paid by Radha

$\implies$ 4500 - 4137.5

$\implies$ Rs 362.5

Therefore, Fabina pays more interest with Rs 362.5 more .