The simple interest on a sum of money at 10% per annum for 2 years is ₹8,000. What will be the compound interest (in ₹) on the same sum for the same period at the same rate compounded annually?
- A8,500
- B8,400
- C8,600
- D8,200
Solution & Step-by-step Explanation
Given:
Simple Interest (SI) = ₹8,000
Rate (R) = 10% per annum
Time (T) = 2 years
We know that:
SI=
100
P×R×T
8000=
100
P×10×2
8000=
100
20P
=
5
P
P=8000×5=₹40,000
Now, we need to calculate the compound interest (CI) on the same principal (P=₹40,000) for 2 years at 10% per annum:
CI=P[(1+
100
R
)
T
−1]
CI=40000[(1+
100
10
)
2
−1]
CI=40000[(1.1)
2
−1]
CI=40000[1.21−1]
CI=40000×0.21=₹8,400
Simple Interest (SI) = ₹8,000
Rate (R) = 10% per annum
Time (T) = 2 years
We know that:
SI=
100
P×R×T
8000=
100
P×10×2
8000=
100
20P
=
5
P
P=8000×5=₹40,000
Now, we need to calculate the compound interest (CI) on the same principal (P=₹40,000) for 2 years at 10% per annum:
CI=P[(1+
100
R
)
T
−1]
CI=40000[(1+
100
10
)
2
−1]
CI=40000[(1.1)
2
−1]
CI=40000[1.21−1]
CI=40000×0.21=₹8,400