sukhman wrote:Compound Interest on a certain sum at a certain rate of interest for the second year is $2400 and for the third year is $ 2880. Find the principal and rate of interest.

Is the answer [spoiler]20% and $10000[/spoiler] ?



Let the interest rate be x% and the principal amts be P1, P2, P3 ...

Between P2 and P3 the interest is incremented by x% :
2400 (1 + x/100) = 2880
x = 20%

Also x% of P2 earns an amount 2400 as the interest, thus P2 * 20% = 2400.
P2 = 12000

Similarly P1 + 20%P1 = P2.
1.20 P1 = 12000
P1 = 10000

sukhman wrote:Compound Interest on a certain sum at a certain rate of interest for the second year is $2400 and for the third year is $ 2880. Find the principal and rate of interest.

When interest is COMPOUNDED annually, the amount of interest earned between successive years increases by the SAME PERCENTAGE as does the principal.

Here, between the 2nd year and the 3rd year, the annual interest increases by the following percent:
(2880-2400)/2400 = 480/2400 = 1/5 = 20%,
Since an ADDITIONAL 20% is earned in the 3rd year, the annual interest rate = 20%, compounded annually.

Let x = the 1st year interest.
Since 2400 -- the 2nd year interest -- is equal to 20% more than the 1st year interest, we get:
2400 = 1.2x
x = 2400/1.2 = 24000/12 = 2000.

Let p = the principal.
Since 2000 -- the 1st year interest -- is equal to 20% of the principal, we get:
2000 = 0.2p
p = 2000/0.2 = 20000/2 = 10000.

Thus:
Principal = 10000, interest rate = 20%, compounded annually.