Aptitude - Compound Interest - Discussion
Discussion Forum : Compound Interest - General Questions (Q.No. 10)
10.
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Answer: Option
Explanation:
| Amount of Rs. 100 for 1 year when compounded half-yearly |
 |
= Rs. |  |
100 x |  |
1 + | 3 |  |
2 |  |
= Rs. 106.09 |
| 100 |
Effective rate = (106.09 - 100)% = 6.09%
Discussion:
43 comments Page 3 of 5.
Zaini said:
6 years ago
How to solve if there is a whole year?
Please explain.
Please explain.
Datta said:
6 years ago
@Durga.
106.09-106 = ?
10690/100 -106 = 6.09.
106.09-106 = ?
10690/100 -106 = 6.09.
Syamu said:
6 years ago
The given interest is 6%.
According to formulae of compound interest for half-yearly [p (1 + (R/2) /100) ^2].
According to formulae of compound interest for half-yearly [p (1 + (R/2) /100) ^2].
Parvathy said:
1 decade ago
Still got no clue. Somebody please explain in simple context. What this effective rate and annual rate anyway?
Jasika said:
1 decade ago
Yeah. How we can find rate by subtracting principal from amount in the form of %?
Sathya said:
1 decade ago
The effective rate is the actual rate that you earn on an investment or pay on a loan after the effects of compounding frequency are considered.
Formula for Effective Rate = (1 + (i / n))^n -1
i = Nominal or stated interest rate
n = Number of compounding periods per year
Formula for Effective Rate = (1 + (i / n))^n -1
i = Nominal or stated interest rate
n = Number of compounding periods per year
Chadrashekhar said:
1 decade ago
Let p=rs 100
As we know that
for yearly:
A=P(1+R/100)^n
=100(1+6/100)
=Rs.106
for half yearly:
A=p(1+R/2*100)^2n
=100(1+6/2*100)^2*1
=100(103/100*103/100)
=Rs.106.09
Effective rate=(106.09-106)=6.09%
As we know that
for yearly:
A=P(1+R/100)^n
=100(1+6/100)
=Rs.106
for half yearly:
A=p(1+R/2*100)^2n
=100(1+6/2*100)^2*1
=100(103/100*103/100)
=Rs.106.09
Effective rate=(106.09-106)=6.09%
Vimal said:
1 decade ago
Thanks chandrashekhar.
Shyamlata said:
1 decade ago
@Chandrashekhar Ji, How could u solve the Effective rate?
= 106.09-106 = 6.09%.
Please explain it.
= 106.09-106 = 6.09%.
Please explain it.
Arun said:
1 decade ago
Effective rate of Interest means,
the simple interest rate that produces the same amount of interest as the compound interest rate.
i.e assume the principal amount be 'x'
Then according to definition,
p*r*t = (p(1+r/100)^n - p),
For S.I., as per question, t= 1 year;
For C.I., as per question, we use formula C.I= (P(1+(r/2)/100)^2 - P);
Therefore,
x*r*1 = ( x(1+(6/2)/100)^2 - x),
r = 0.0609;
or, rate percent = 6.09.
the simple interest rate that produces the same amount of interest as the compound interest rate.
i.e assume the principal amount be 'x'
Then according to definition,
p*r*t = (p(1+r/100)^n - p),
For S.I., as per question, t= 1 year;
For C.I., as per question, we use formula C.I= (P(1+(r/2)/100)^2 - P);
Therefore,
x*r*1 = ( x(1+(6/2)/100)^2 - x),
r = 0.0609;
or, rate percent = 6.09.
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