Sabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Rabiya 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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Answers
Answer:
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Step-by-step explanation:
Sabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Rabiya 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:
Here, Principal (P) = Rs.12,500, Time (T) = 3 years, Rate of interest (R) = 12% p.a.
Simple interest for Fabina = \frac{P\times R\times T}{100}=\frac{12500\times12\times3}{100}=\ Rs.\ 4,500
100
P×R×T
=
100
12500×12×3
= Rs. 4,500
Amount for Radha, P = Rs. 12,500, R = 10% and n = 3 years
Amount (A) = P\left(1+\frac{R}{100}\right)^nP(1+
100
R
)
n
= 12500\left(1+\frac{10}{100}\right)^3=12500\left(1+\frac{1}{10}\right)^312500(1+
100
10
)
3
=12500(1+
10
1
)
3
= 12500\left(\frac{11}{10}\right)^2=12500\times\frac{11}{10}\times\frac{11}{10}\times\frac{11}{10}12500(
10
11
)
2
=12500×
10
11
×
10
11
×
10
11
= Rs. 16,637.50
\therefore∴ C.I. for Radha = A – P
= Rs. 16,637.50 – Rs. 12,500 = Rs. 4,137.50
Here, Fabina pays more interest
= Rs. 4,500 – Rs. 4,137.50 = Rs. 362.50