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?​

Answer 1

Given :

For Fabina :

• ➻P = ₹ 12,500
• ➻R = 12% p.a.
• ➻n = 3 years

For Radha :

• ➻P = ₹ 12,500
• ➻R = 10% p.a.
• ➻n = 3 years

To Find :

The intrest who pays the more and how much?

Solution:

$\rule{200pt}{2pt}$

$\rm{SI = \dfrac{P \times R \times n}{100}}$

$\dashrightarrow\dfrac{12,500 \times 12 \times 3}{1 00}$

$\dashrightarrow\dfrac{12,5 \cancel{00} \times 12 \times 3}{1 \cancel { 00}}$

$\dashrightarrow \: ₹4500$

$\rule{200pt}{2pt}$

For Radha :

$\rm{CI = A-P}$

$\dashrightarrow \rm{P \bigg\lgroup 1+ \rm\dfrac{R}{100} \bigg\rgroup ^{n} - P}$

$\dashrightarrow 12,500\bigg \{1 + \dfrac{10}{1 00} \bigg \} ^{3} -12,500$

$\dashrightarrow 12500\bigg \{\dfrac{100 + 10}{1 00} \bigg \} ^{3} -12,500$

$\dashrightarrow 12500\bigg \{ \cancel \dfrac{ 110}{100} \bigg \} ^{3} -12,500$

$\dashrightarrow 12,500\bigg \{ \dfrac{ 11}{10} \bigg \} ^{3} -12,500$

$\dashrightarrow 12500 \times \dfrac{ 11 \times 11 \times 11}{10 \times 10 \times 10} -12500$

$\dashrightarrow 12500 \times \dfrac{ 1331}{1000} -12,500$

$\dashrightarrow 12500 \bigg \{ \dfrac{ 1331}{1000} \bigg \} - 12500$

$\dashrightarrow 125 \cancel{00 }\bigg \{ \dfrac{ 1331 }{1 0 \cancel{00}} \bigg \} - 12500$

$\dashrightarrow \cancel{ 125 }\bigg \{ \dfrac{ 1331 }{ \cancel{1 0 }} \bigg \} - 12500$

$\dashrightarrow 12.5 \times 1331 - 12500$

$\dashrightarrow ₹4137.50$

Difference between the intrests = ₹4500 - ₹4137.5

= ₹362.5

∴ Fabina Pays More intrest --- ₹362.5

$\rule{211pt}{8pt}$

Answer 2

Answer:

• ➝ Fabina paid more interest than Radha.
• ➝ Fabina paid Rs.362.50 more than Radha.

Step-by-step explanation :

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?

$\begin{gathered}\end{gathered}$

Solution :

Calculating the simple interest paid by Fabina.

• ✧ Principle = Rs.12500
• ✧ Rate = 12% per annum
• ✧ Time = 3 years

Substituting the values in the formula :

${\implies{\sf{S.I = \dfrac{P \times R \times T}{100}}}}$

${\implies{\sf{S.I = \dfrac{12500\times 12\times 3}{100}}}}$

${\implies{\sf{S.I = \dfrac{12500\times 36}{100}}}}$

${\implies{\sf{S.I = \dfrac{450000}{100}}}}$

${\implies{\sf{S.I = \cancel{\dfrac{450000}{100}}}}}$

${\implies{\sf{\underline{\underline{\red{S.I = Rs.4500}}}}}}$

Hence, the simple interest is Rs.4500.

$\begin{gathered}\end{gathered}$

Calculating the compound interest paid by Radha.

• ✧ Principle = Rs.12500
• ✧ Rate = 10% per annum
• ✧ Time = 3 years

Substituting the values in the formula :

${\implies{\sf{C.I = P \bigg[1 + \dfrac{R}{100} \bigg]^{T} - P}}}$

${\implies{\sf{C.I = 12500 \bigg[1 + \dfrac{10}{100} \bigg]^{3} - 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[\dfrac{100 + 10}{100} \bigg]^{3} - 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[\dfrac{110}{100} \bigg]^{3} - 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[ \cancel{\dfrac{110}{100}} \bigg]^{3} - 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[ \: \dfrac{11}{10} \: \bigg]^{3} - 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[ \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \bigg]- 12500}}}$

${\implies{\sf{C.I = 12500 \bigg[ \dfrac{1331}{1000}\bigg]- 12500}}}$

${\implies{\sf{C.I = 12500 \times \dfrac{1331}{1000}- 12500}}}$

${\implies{\sf{C.I = \cancel{12500} \times \dfrac{1331}{\cancel{1000}}- 12500}}}$

${\implies{\sf{C.I = 12.5 \times 1331 - 12500}}}$

${\implies{\sf{C.I = 16637.5 - 12500}}}$

${\implies{\sf{\underline{\underline{\red{C.I = Rs.4137.50}}}}}}$

Hence, the compound interest is Rs.4137.50.

$\begin{gathered}\end{gathered}$

Since, we can see that :

• ➝ Fabina > Radha
• ➝ 4500 > 4137.50,

Hence Fabina paid more interest than Radha.

$\begin{gathered}\end{gathered}$

Now, calculating the how much interest paid by Fabina more than Radha :

${\implies{\sf{Interest \: Paid = Fabina - Radha}}}$

${\implies{\sf{Interest \: Paid = 4500 - 4137.50}}}$

${\implies{\sf{\underline{\underline{\red{Interest \: Paid = 362.50}}}}}}$

Hence, the Fabina paid Rs.362.50 more than Radha.

$\begin{gathered}\end{gathered}$

Learn More :

$\longrightarrow\small{\underline{\boxed{\sf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Amount = Principle + Interest}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{ Principle=Amount - Interest }}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Time = \dfrac{Simple \: Interest \times 100}{Principle \times Rate}}}}}$

$\underline{\rule{220pt}{3.5pt}}$