A sum of money on compound interest amounts to Rs. 13,200 in 2 years and Rs. 14,520 in 3 years. What is the rate of interest per annum?
- A8%
- B10%
- C9%
- D7%
Solution & Step-by-step Explanation
Let the principal be P and the annual rate of interest be R%.
The amount after 2 years is A
2
=Rs. 13,200.
The amount after 3 years is A
3
=Rs. 14,520.
In compound interest, the amount at the end of the 2nd year acts as the principal for the 3rd year.
Therefore, the interest earned in the 3rd year is:
Interest=A
3
−A
2
=14,520−13,200=Rs. 1,320
Now, we can find the rate of interest (R):
Interest=
100
A
2
×R×1
1,320=
100
13,200×R
1,320=132×R
R=
132
1,320
=10%
Thus, the rate of interest per annum is 10%.
The amount after 2 years is A
2
=Rs. 13,200.
The amount after 3 years is A
3
=Rs. 14,520.
In compound interest, the amount at the end of the 2nd year acts as the principal for the 3rd year.
Therefore, the interest earned in the 3rd year is:
Interest=A
3
−A
2
=14,520−13,200=Rs. 1,320
Now, we can find the rate of interest (R):
Interest=
100
A
2
×R×1
1,320=
100
13,200×R
1,320=132×R
R=
132
1,320
=10%
Thus, the rate of interest per annum is 10%.