What will be the compound interest on a sum of ₹3,750 when interest is compounded semi-annually at 16% per annum for one year?
- A₹600
- B₹650
- C₹640
- D₹624
Solution & Step-by-step Explanation
Given:
Principal (P) = ₹3,750
Annual Rate (R) = 16% per annum
Time (T) = 1 year
Since the interest is compounded semi-annually:
New Rate (R
′
) =
2
16%
=8% per half-year
New Time (n) = 1×2=2 half-years
The formula for the total amount (A) is:
A=P(1+
100
R
′
)
n
A=3750(1+
100
8
)
2
A=3750(
100
108
)
2
=3750(
25
27
)
2
A=3750×
625
729
Since
625
3750
=6:
A=6×729=₹4374
Now, Compound Interest (CI) is:
CI=A−P=4374−3750=₹624
Principal (P) = ₹3,750
Annual Rate (R) = 16% per annum
Time (T) = 1 year
Since the interest is compounded semi-annually:
New Rate (R
′
) =
2
16%
=8% per half-year
New Time (n) = 1×2=2 half-years
The formula for the total amount (A) is:
A=P(1+
100
R
′
)
n
A=3750(1+
100
8
)
2
A=3750(
100
108
)
2
=3750(
25
27
)
2
A=3750×
625
729
Since
625
3750
=6:
A=6×729=₹4374
Now, Compound Interest (CI) is:
CI=A−P=4374−3750=₹624