what is the formula for compound interest for loans etc?

Answer 1

CI= P{(1+r)^T-1}

where,
CI is compound interest
P is principal sum borrowed
r is rate of interest
T is time elapsed

r and T must correspond, which means that if rate of interest is 5% compounded annually then for a 3 year period, r=0.05 and T=3 whereas if it is 5% p.a. compounded half-yearly then r=0.025 and T=6 for the same period.
Note that this formula gives the total CI after the T time. It does not take into account any repayments done during that period. For EMI etc. better check the banks and their policies!

Answer 2

Sourabh's answer is exceptional. It works for bonds and most investments.

There is one addition I would like to make. Banks use what is called "actual/360" day counting. That means that they take the stated yield and divide by 360 -- then raise it to the actual number of days.

Suppose you put 1000 into a bank that pays 5%. At the end of one year, you will have:

1000 * (1+5%/360) ^ 365

It is a little odd, but it is what they do.