Simple v/s Compound Interest

Interest is what you earn when you let people borrow your money.  Some call it the price of renting your money.  Obviously how much you will rent it for will depend on many things and mainly on the differences between simple and compound interest.

Simple Interest is, well, the simplest and most basic kind of interest out there. You can calculate simple interest by multiplying Principal by Rate by Time, given by the following formula:

Simple Interest (SI) = (P * R * T)/100

P = principal amount (the amount that was borrowed)
r = rate of interest (for one period)
t = time duration for which the money is borrowed (number of periods)

Here, principal (P) is the amount to begin with, whether it's invested, lent, or borrowed. This amount increases by the given interest rate (r) over a period of time (t). To calculate not just the accrual but the resulting amount to which interest is applied, you can use the amount function:

A(t) = A₀ x (1 + t x r)

In the given formula, A₀ is the principal, while r and t are the interest rate and period of time, respectively.

Because simple interest is a linear function, it is quite easy to see how a loan or an investment will turn out in the future.

Compound Interest is a bit more tricky to calculate. Interest is periodically added to the current amount, and the amount you get (or owe) is computed from the following formula:

Compound Interest (CI) = P(1+r/n)^nt

P = principal amount, (either borrowed or deposited)
r = rate of interest (annual/quarterly/half yearly)
n = numbers of times the interest is compounded every year
t = number of years (period) the amount is deposited for

To calculate the resulting amount to which interest is applied, you can use the amount function:

A(t) = A₀ x (1 + r/n)n x t

The principal (A₀) increases by an amount that is dependent on both the given interest rate (r) and the number of compounding periods (n) within a given time period. This time (t) is usually expressed in years. So if a starting amount, Rs 500 were to be compounded at a monthly rate of 5% for five years, n would be equal to 12 and t would be equal to 5. The equation would be: A(t) = 500 x (1 + 0.05/12)5 x 12 and amounts to Rs 641.68.

Instead of a linear rate being applied, we see an exponential growth: notice that each time the amount A(t) is compounded by an interest rate dependent on that current amount A(t). In investing, that sounds like a good way to make your money grow. In borrowing, however, that doesn't sound that great.

It is tricky to figure out the additional amount added to the principal in a compounded interest scheme, calculating the annual percentage yield or APY can be a helpful method in calculating the yield, or the extra amount, and not the total resulting amount. You can get your APY through the following equation:

APY = (1 + r/n)n – 1

Again, r stands for the interest rate and n is the frequency of compounding that occurs in a year. Calculating APY gives you a better idea of how much you earn or how much more you owe in relation to the principal.

The difference between simple and compound interest is the difference between night and day. You will want to remember this simple rule: simple interest grows slowly, compounding speeds up the process. 

Simple interest is interest on the principle amount while compound interest is when your principle and any earned interest earned interest. If you have invested money into an account you always want compound interest. Moreover, the relative advantages of compound interest escalate as your holding period increases.

Therefore, before investing your money, you should double check with your local bank if compound interest will be used.

Having said that if you have a credit card and you owe money on it, you will pay less interest if the credit card company uses simple interest. However, they will never do something so foolish!

I hope simple vs compound interest is well understood now... :-)