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Certain sum was lent at compound interest, compounded annually for three years. The rate of interest for each of the three years was 20%, 15% and 10% p.a. respectively. If the same sum was lent at a constant rate of simple interest for the same period, then what would have been the interest rate for obtaining the same amount of interest?
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Certain sum was lent at compound interest, compounded annually for thr...
Solution:
Compound Interest Calculation:
Let the principal amount be P.
For the first year, the interest is calculated at a rate of 20%. Therefore, the principal amount for the second year will be P*(1+20/100) = P*1.2.
For the second year, the interest is calculated at a rate of 15%. Therefore, the principal amount for the third year will be P*1.2*(1+15/100) = P*1.38.
For the third year, the interest is calculated at a rate of 10%. Therefore, the amount at the end of 3 years will be P*1.38*(1+10/100) = P*1.518.
Hence, the compound interest earned in 3 years is P*0.518.
Simple Interest Calculation:
Let the rate of interest be R%.
Using the formula for simple interest, the interest earned in 3 years is P*(3*R/100).
Equating the compound interest and simple interest, we get:
P*0.518 = P*(3*R/100)
R = 17.27%
Therefore, the rate of interest for obtaining the same amount of interest using simple interest is 17.27%.
Explanation:
Compound interest is the interest earned on both the principal amount and the interest earned in the previous periods. Therefore, the effective interest rate is higher than the nominal interest rate.
On the other hand, simple interest is calculated only on the principal amount. Therefore, the effective interest rate is lower than the nominal interest rate.
In this question, we are given the nominal interest rates for each of the three years and asked to find the effective interest rate for obtaining the same amount of interest using simple interest.
By equating the compound interest and simple interest, we can find the effective interest rate using simple interest. In this case, the effective interest rate using simple interest is lower than the nominal interest rates for each of the three years.
Therefore, we can conclude that compound interest is more beneficial for the lender than simple interest.
Compound Interest Calculation:
Let the principal amount be P.
For the first year, the interest is calculated at a rate of 20%. Therefore, the principal amount for the second year will be P*(1+20/100) = P*1.2.
For the second year, the interest is calculated at a rate of 15%. Therefore, the principal amount for the third year will be P*1.2*(1+15/100) = P*1.38.
For the third year, the interest is calculated at a rate of 10%. Therefore, the amount at the end of 3 years will be P*1.38*(1+10/100) = P*1.518.
Hence, the compound interest earned in 3 years is P*0.518.
Simple Interest Calculation:
Let the rate of interest be R%.
Using the formula for simple interest, the interest earned in 3 years is P*(3*R/100).
Equating the compound interest and simple interest, we get:
P*0.518 = P*(3*R/100)
R = 17.27%
Therefore, the rate of interest for obtaining the same amount of interest using simple interest is 17.27%.
Explanation:
Compound interest is the interest earned on both the principal amount and the interest earned in the previous periods. Therefore, the effective interest rate is higher than the nominal interest rate.
On the other hand, simple interest is calculated only on the principal amount. Therefore, the effective interest rate is lower than the nominal interest rate.
In this question, we are given the nominal interest rates for each of the three years and asked to find the effective interest rate for obtaining the same amount of interest using simple interest.
By equating the compound interest and simple interest, we can find the effective interest rate using simple interest. In this case, the effective interest rate using simple interest is lower than the nominal interest rates for each of the three years.
Therefore, we can conclude that compound interest is more beneficial for the lender than simple interest.
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Certain sum was lent at compound interest, compounded annually for three years. The rate of interest for each of the three years was 20%, 15% and 10% p.a. respectively. If the same sum was lent at a constant rate of simple interest for the same period, then what would have been the interest rate for obtaining the same amount of interest?
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Certain sum was lent at compound interest, compounded annually for three years. The rate of interest for each of the three years was 20%, 15% and 10% p.a. respectively. If the same sum was lent at a constant rate of simple interest for the same period, then what would have been the interest rate for obtaining the same amount of interest? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Certain sum was lent at compound interest, compounded annually for three years. The rate of interest for each of the three years was 20%, 15% and 10% p.a. respectively. If the same sum was lent at a constant rate of simple interest for the same period, then what would have been the interest rate for obtaining the same amount of interest? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Certain sum was lent at compound interest, compounded annually for three years. The rate of interest for each of the three years was 20%, 15% and 10% p.a. respectively. If the same sum was lent at a constant rate of simple interest for the same period, then what would have been the interest rate for obtaining the same amount of interest?.
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