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The effective rate of interest corresponding a nominal rate of 7% p.a convertible quarterly is
- a)7%
- b)7.5%
- c)7.10%
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The effective rate of interest corresponding a nominal rate of 7% p.a ...
r = 7% p.a i.e 1.75% per quarter(7/4). so 1+reff = (1.0175)^4 = 1.071859 implies reff = 7.1859
Most Upvoted Answer
The effective rate of interest corresponding a nominal rate of 7% p.a ...
I = 7/4(quarterly) = 1.75/100= 0.0175
E=(1+0.0175)^4 - 1
E=(1.071859) - 1
E=0.07185 × 100
E= 7.18%
E=(1+0.0175)^4 - 1
E=(1.071859) - 1
E=0.07185 × 100
E= 7.18%
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The effective rate of interest corresponding a nominal rate of 7% p.a ...
Calculation of Effective Rate of Interest
Nominal rate of interest refers to the rate of interest mentioned in the contract or agreement between the borrower and the lender. However, the effective rate of interest takes into account the compounding frequency of interest.
In this case, the nominal rate of interest is 7% p.a convertible quarterly, which means that the interest is compounded every quarter. To calculate the effective rate of interest, we use the following formula:
Effective Rate of Interest = (1 + Nominal Rate/n)^n - 1
where n is the number of compounding periods in a year.
Substituting the values, we get:
Effective Rate of Interest = (1 + 7%/4)^4 - 1
Effective Rate of Interest = (1 + 0.0175)^4 - 1
Effective Rate of Interest = 1.0175^4 - 1
Effective Rate of Interest = 0.0741 or 7.41%
Therefore, the effective rate of interest corresponding to a nominal rate of 7% p.a convertible quarterly is 7.41%.
Answer Option
The correct answer is option 'D' none of these as none of the given options matches with the calculated effective rate of interest.
Nominal rate of interest refers to the rate of interest mentioned in the contract or agreement between the borrower and the lender. However, the effective rate of interest takes into account the compounding frequency of interest.
In this case, the nominal rate of interest is 7% p.a convertible quarterly, which means that the interest is compounded every quarter. To calculate the effective rate of interest, we use the following formula:
Effective Rate of Interest = (1 + Nominal Rate/n)^n - 1
where n is the number of compounding periods in a year.
Substituting the values, we get:
Effective Rate of Interest = (1 + 7%/4)^4 - 1
Effective Rate of Interest = (1 + 0.0175)^4 - 1
Effective Rate of Interest = 1.0175^4 - 1
Effective Rate of Interest = 0.0741 or 7.41%
Therefore, the effective rate of interest corresponding to a nominal rate of 7% p.a convertible quarterly is 7.41%.
Answer Option
The correct answer is option 'D' none of these as none of the given options matches with the calculated effective rate of interest.
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