Interest Rates: Simple and Compound

Interest is a fee charged by banks for borrowing funds. Also, this is extra money you can earn depositing money into a savings account. For both loans and deposits, the ultimate amount exceeds the principal amount. In banking, the principal is defined as the original amount of money lent or borrowed, which is used to calculate interest. There are two types of interest. They differ in the way they’re calculated: simple and compound.

Simple interest

It is charged on the principal amount of a loan with no compounding effect. Simple interest is calculated using the formula:

p × i × t = I_s

where

p is the principal amount borrowed or lent

i is the interest rate or the percentage charged on the principal (converted into a decimal form)

t is the number of periods

I_s is simple interest on a loan or deposit over a period of time

So, this deposit will bring $300 for the whole period of 3 years.

Compound Interest

Also referred to as ‘interest on interest‘, this is charged on the principal amount plus all the interest accruing over time. Compound interest is calculated using the formula below:

p (1 + i)ⁿ – p = I_c

where

p is the principal amount borrowed or lent

i is the interest rate per period (converted into a decimal form)

n is the number of compounding periods

I_c is compound interest on a loan or deposit

So, $315.25 is the amount that the deposited sum produces over 3 years. Now, compare the results from the two examples. Note that the compounding effect generates a bigger amount than simple interest does. This means that you will lose more on loan and earn more on deposit if the interest works out on a compound ground.

Take into consideration the compounding periods when calculating interest. If it is charged more than once a year, make sure you insert the correct values for ‘i’ and ‘n’ into the formula. For example, if the interest on a 6-year loan with the rate of 4% is compounded twice per year, then the number of periods (t) will be 6x2=12 and the interest rate per period (n) will be 4%/2=2%.

Now, suppose you’ve made an investment with the interest compounded annually. If you want to figure out when it will double, use the rule of 72. Simply divide 72 by the interest rate. For example, an investment with 4% rate will double in 18 years.

Conclusion

Compound interest is always greater than simple interest. Compounding works in your favour when you invest and against you when you take a loan. People compare interest rates when choosing a lender or a credit card issuer. However, these figures don’t show the full picture. Instead, consider the Annual Percentage Rate (APR). It includes both interest rates and extra payments, such as origination or closing fees.