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An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
- a)10%
- b)10.25%
- c)10.5%
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An automobile financier claims to be lending money at simple interest,...
B is the correct option. Solution
6 months interest will be 5%
next 6 months interest will be 5%
percentage effect = 5 + 5 +25/100
= 10.25 Ans
6 months interest will be 5%
next 6 months interest will be 5%
percentage effect = 5 + 5 +25/100
= 10.25 Ans
Most Upvoted Answer
An automobile financier claims to be lending money at simple interest,...
6 months interest will be 5%
next 6 months interest will be 5%
percentage effect = 5 + 5 +25/100
= 10.25 Ans
next 6 months interest will be 5%
percentage effect = 5 + 5 +25/100
= 10.25 Ans
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Community Answer
An automobile financier claims to be lending money at simple interest,...
Calculation of Interest
Simple Interest Calculation:
- The formula for simple interest is I = PRT, where I = Interest, P = Principal, R = Rate of interest, and T = Time.
- Here, the principal remains constant throughout the loan tenure, and the interest is calculated only on the initial principal amount.
Interest Calculation by the Financier:
- The financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal.
- Let's consider a loan of Rs. 100 for one year at 10% simple interest.
- According to simple interest, the interest charged for one year would be Rs. 10.
- But the financier calculates interest every six months and adds it to the principal.
- After six months, the interest charged would be Rs. 5 (10% of Rs. 100/2).
- The principal for the second half of the year would be Rs. 105 (Rs. 100 + Rs. 5).
- At the end of the year, the interest charged would be Rs. 10.5 (10% of Rs. 105).
- Hence, the total amount to be repaid would be Rs. 115.5 (Rs. 100 + Rs. 10.5).
Effective Rate of Interest
- The effective rate of interest is the actual interest rate charged on a loan or investment.
- It takes into account the compounding of interest over a period of time.
- In this case, the interest is compounded every six months, and hence, the effective rate of interest would be higher than 10%.
Calculation of Effective Rate of Interest:
- Let's consider the same loan of Rs. 100 at 10% simple interest, but calculated as per the financier's method.
- The principal for the first half of the year would be Rs. 100.
- After six months, the interest charged would be Rs. 5 (10% of Rs. 100/2) and added to the principal, making it Rs. 105.
- The principal for the second half of the year would be Rs. 105.
- At the end of the year, the interest charged would be Rs. 5.25 (10% of Rs. 105/2).
- Hence, the total amount to be repaid would be Rs. 110.25 (Rs. 100 + Rs. 5.25).
- The effective rate of interest can be calculated using the formula: ((Total amount to be repaid / Principal) - 1) x 100
- In this case, the effective rate of interest would be ((110.25/100) - 1) x 100 = 10.25%
Hence, the correct answer is option B, i.e., 10.25%.
Simple Interest Calculation:
- The formula for simple interest is I = PRT, where I = Interest, P = Principal, R = Rate of interest, and T = Time.
- Here, the principal remains constant throughout the loan tenure, and the interest is calculated only on the initial principal amount.
Interest Calculation by the Financier:
- The financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal.
- Let's consider a loan of Rs. 100 for one year at 10% simple interest.
- According to simple interest, the interest charged for one year would be Rs. 10.
- But the financier calculates interest every six months and adds it to the principal.
- After six months, the interest charged would be Rs. 5 (10% of Rs. 100/2).
- The principal for the second half of the year would be Rs. 105 (Rs. 100 + Rs. 5).
- At the end of the year, the interest charged would be Rs. 10.5 (10% of Rs. 105).
- Hence, the total amount to be repaid would be Rs. 115.5 (Rs. 100 + Rs. 10.5).
Effective Rate of Interest
- The effective rate of interest is the actual interest rate charged on a loan or investment.
- It takes into account the compounding of interest over a period of time.
- In this case, the interest is compounded every six months, and hence, the effective rate of interest would be higher than 10%.
Calculation of Effective Rate of Interest:
- Let's consider the same loan of Rs. 100 at 10% simple interest, but calculated as per the financier's method.
- The principal for the first half of the year would be Rs. 100.
- After six months, the interest charged would be Rs. 5 (10% of Rs. 100/2) and added to the principal, making it Rs. 105.
- The principal for the second half of the year would be Rs. 105.
- At the end of the year, the interest charged would be Rs. 5.25 (10% of Rs. 105/2).
- Hence, the total amount to be repaid would be Rs. 110.25 (Rs. 100 + Rs. 5.25).
- The effective rate of interest can be calculated using the formula: ((Total amount to be repaid / Principal) - 1) x 100
- In this case, the effective rate of interest would be ((110.25/100) - 1) x 100 = 10.25%
Hence, the correct answer is option B, i.e., 10.25%.
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An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:a)10%b)10.25%c)10.5%d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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