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The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is
- a)3.2% p.a
- b)3.25% p.a
- c)3.0225% p.a
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The effective rate of interest corresponding to a nominal rate 3% p.a ...
The amount after 1 year at 8% per annum when interest is compounded half yearly is
=100(1+3/2/100)2×1=100(101.5/100)2=103.0225
CI for 1 year = 103.0225 – 100 = 3.0225
The effective annual rate of interest is = 3.0225%
=100(1+3/2/100)2×1=100(101.5/100)2=103.0225
CI for 1 year = 103.0225 – 100 = 3.0225
The effective annual rate of interest is = 3.0225%
Most Upvoted Answer
The effective rate of interest corresponding to a nominal rate 3% p.a ...
R=3%
Interest paid 2 times in an year
Then I = R|K = 3|2 %=1.5%=0.015
By the formula
E=(1+i)^n
=> E= (1+0.015)^2 -1
=> E= (1.015)^2 -1
=> E= 1.03025 -1 = 0.03025 or
0.03025�100 = 3.025% ans
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The effective rate of interest corresponding to a nominal rate 3% p.a ...
Effective Rate of Interest:
The effective rate of interest is the actual rate of interest earned or paid on an investment or loan after taking into account the effects of compounding. It is the rate at which money actually grows in value over a year.
Nominal Rate of Interest:
The nominal rate of interest is the stated rate of interest that does not take into account the effects of compounding. It is the rate at which interest is calculated on an annual basis.
Calculation of Effective Rate of Interest:
To calculate the effective rate of interest, we use the formula:
Effective rate of interest = (1 + (nominal rate / m))^m - 1
Where,
m = number of compounding periods in a year
nominal rate = stated rate of interest
In this question, the nominal rate of interest is 3% p.a payable half yearly. Therefore, the compounding period is half-yearly (m = 2).
Substituting the values in the formula, we get:
Effective rate of interest = (1 + (3/2))^2 - 1
= (1.015)^2 - 1
= 1.030225 - 1
= 0.030225 or 3.0225%
Therefore, the correct option is (c) 3.0225% p.a.
The effective rate of interest is the actual rate of interest earned or paid on an investment or loan after taking into account the effects of compounding. It is the rate at which money actually grows in value over a year.
Nominal Rate of Interest:
The nominal rate of interest is the stated rate of interest that does not take into account the effects of compounding. It is the rate at which interest is calculated on an annual basis.
Calculation of Effective Rate of Interest:
To calculate the effective rate of interest, we use the formula:
Effective rate of interest = (1 + (nominal rate / m))^m - 1
Where,
m = number of compounding periods in a year
nominal rate = stated rate of interest
In this question, the nominal rate of interest is 3% p.a payable half yearly. Therefore, the compounding period is half-yearly (m = 2).
Substituting the values in the formula, we get:
Effective rate of interest = (1 + (3/2))^2 - 1
= (1.015)^2 - 1
= 1.030225 - 1
= 0.030225 or 3.0225%
Therefore, the correct option is (c) 3.0225% p.a.
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