Fabulous borrow s ₹12500 at 12% per annual for 3 years at simple interest and Radio borrow s the same amount for the same period at 10% per annum compounded annualy.Who pays more interest and by how much?
Answers
Correct 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:-
Given:
For Fabina :
Principal (P) = Rs. 12500
Rate of interest (R) = 12 %
Time period (T) = 3 years.
We know that,
Simple interest (SI) = PTR/100
So,
SI = (12500)(3)(12)/100
⟶ SI = Rs. 4500
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For Radha :
Principal (P) = Rs. 12500
Rate of interest (R) = 10 %
Time period (n) = 3 years.
We know,
Compound interest (CI) = P (1 + R/100)ⁿ - P
So,
⟶ CI = 12500(1 + 10/100)³ - 12500
⟶ CI = 12500 * (110/100)³ - 12500
⟶ CI = [ (12500)(110)(110)(110)/1000000 ] - 12500
⟶ CI = 16637.5 - 12500
⟶ CI = Rs. 4137.5
We observe that,
Interest paid by Fabina is more than the interest paid by Radha.
So, difference between the amount paid by them = 4500 - 4137.5 = Rs. 362.5
∴ Fabina pays more interest than Radha by Rs. 362.5
Step-by-step explanation:
Given:
- → Fabiana 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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Solution :
- → 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.