A sum of ₹ 1,000 becomes ₹ 1,144.90 in 2 years. At what rate is the interest compounded annually?
- A7%
- B5%
- C8%
- D6%
Solution & Step-by-step Explanation
The formula for the amount under annual compound interest is:
A=P(1+
100
R
)
T
Given parameters:
Principal (P) = ₹ 1,000
Amount (A) = ₹ 1,144.90
Time (T) = 2 years
Substitute the values into the formula:
1144.90=1000(1+
100
R
)
2
1000
1144.90
=(1+
100
R
)
2
1.1449=(1+
100
R
)
2
Taking the square root on both sides:
1.1449
=1+
100
R
1.07=1+
100
R
100
R
=1.07−1
100
R
=0.07
R=7%
Therefore, the annual compounding interest rate is 7%.
A=P(1+
100
R
)
T
Given parameters:
Principal (P) = ₹ 1,000
Amount (A) = ₹ 1,144.90
Time (T) = 2 years
Substitute the values into the formula:
1144.90=1000(1+
100
R
)
2
1000
1144.90
=(1+
100
R
)
2
1.1449=(1+
100
R
)
2
Taking the square root on both sides:
1.1449
=1+
100
R
1.07=1+
100
R
100
R
=1.07−1
100
R
=0.07
R=7%
Therefore, the annual compounding interest rate is 7%.