Interest

[sukhman]

Compound interest on a certain sum at a certain rate of interest for the second year is $2400 and for third year is is $ 2880. Find the principal in $.
a) 10000 b) 5000 c)4000 d)9500 e)4500

[GMATGuruNY]

Compound interest on a certain sum at a certain rate of interest for the second year is $2400 and for third year is is $ 2880. Find the principal in $.
a) 10000 b) 5000 c)4000 d)9500 e)4500

(3rd-year interest) - (2nd-year interest) = 2880 - 2400 = 480.
The 3rd-year interest is $480 greater because -- in the 3rd year -- interest is earned not only on the amount at the end of the first year but also on the interest earned in the 2nd year.
Since 480 is equal to 20% of 2400, the interest rate is likely to be 20%.

We can PLUG IN THE ANSWERS, which represent the principal.
When the correct answer choice is plugged in, the interest in the 2nd year will be $2400.
Since the 1st-year interest must be a bit less than the 2nd-year interest of $2400 -- and 20% of 10,000 is equal to $2000 -- the correct answer is probably A.

A: 10,000
1st-year interest = 20% of 10,000 = 2000.
Amount at the end of the 1st year = 10,000 + 2,000 = 12,000.
2nd-year interest = 20% of 12,000 = 2400.
Success!

The correct answer is A.