Simple and Compound Interest

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Money has purchasing power and earning power. When you make these powers work for you, you are winning, but when these powers work against you, you are losing.

When you need to make a large purchase but you do not have the funds to pay for it right away, banks will lend you the money. Banks will impose charges or fees to have the money available to you. Those charges or fees are called interest.


Banks make their profits in many ways, one of them is lending you other people’s money. Banks attract people’s money and pay interest when people deposit their money into their bank accounts. When you need money, banks take other people’s money and lend it to you charging you a fee, a.k.a an interest.

Two methods have evolved in calculating the interest on money by banks and financial institutions. These are simple interest and compound interest.

Simple Interest

Banks or financial institutions are no longer using simple interest in their practices. When you understand the difference between simple interest and compound interest, you will understand why.

Simple interest is calculated on money by applying the interest charge on the original sum only, no matter how long the money is borrowed.

As an example, let’s say you deposit $5,000 in a bank account under 5 % simple interest per year for 3 years.

The formula to calculate simple interest is simple as the interest itself:

Step 1: Find interest earned in one year

(initial sum) x (interest rate per year) = (interest earned in the first year)
Plug in the numbers from the example to the formula:
$5,000 x 5% = $250
$5,000 deposited under 5% simple interest earn $250 per year.

Step 2: Find interest earned in 3-year term

(interest earned per year) x (term) = (total interest earned in full term)
$250 x 3 = $750

At the end of the term, the bank will return you the originally invested amount of $5,000 plus the interest earned in 3 years, which is $750, or $5,750.

And that is it… Simple interest.

Economists, business analysts, and overall financial engineers use this formula to quickly find the final amount:

Simple Interest Formula Explained Click To Tweet

F =P(1 + i x n), where:

F = the final amount (principal and interest)

P = the original sum, or initial amount, or the principal

i = interest rate as a decimal. i = (annual interest rate 5% in this case /100)

n = number of years for which the amount is deposited

F = $5,000(1 + 0.05 x 3)

F = $5,750

Compound Interest

The compound interest, on the other hand, is the interest on the interest. The interest earned every year is added to the original sum and then is calculated based on the new sum.


To illustrate, let’s continue with the same example as the one for the simple interest.

Step 1: Find an interest earned in the first year

$5,000 deposited under 5% compound interest earn $250 per year.

Step 2: With the compound interest, the bank will add first-year earnings to the original sum and calculate interest earned for the second year

(initial sum at the start of the 2nd year) x (interest rate per year)=(interest earned at the end of the 2nd year)
$5,250 x 5% = $5,512.50

Step 3: Find interest earned in the 3rd year by calculating compound interest on the sum at the end of the second year

$5,512.50 x 5% = $5,788.12

The professional financial formula to calculate the final amount with compound interest is:

Compound Interest Formula Explained Click To Tweet

F = Vn = P x (1 + i) n , where:

F = the final amount at the end of the n years

Vn = value is also equal to the value at the end of the nth year, which is the future value F.

i = interest rate as a decimal. i = (annual interest rate 5% in this case /100)

n = number of years for which the amount is deposited

F = Vn = $5,000 x (1 + 0.05) 3

F = $5,788.12

The difference between simple and compound interest is obvious. $38.12 in this example is interest earned on top of interest on the original sum.

Compound interest is an attractive earning power when compound interest works for you, meaning when you rip the benefits of compound interest.

Compound interest is painful when it works against you. Credit card companies use compound interest on all purchases you made with your credit cards.

Credit cards provide you with unsecured funds whenever you need them. For that, credit cards charge the highest interest possible based on your trustworthiness and ability to repay the debt. After all, credit cards finance the risk associated with your ability to repay.

As an example, suppose you have a credit card with a 27% interest rate. You made a purchase in the amount of $1,000. If you will be unable to pay off that amount during your grace period, by the due date, you will be paying a sum of compound interest and a fraction of a principle amount.

To illustrate:

Step 1: Find out how much each day of keeping the amount on a credit card will cost you

(initial amount) x (interest rate)/ 365 days
$1,000 x 27% /365 = $0.74 cents per day

Step 2: Calculate the amount you will need to pay on top of the initial amount if the amount is not paid in full

(initial amount) + (interest amount per day) * ( days in your billing cycle. For this example 30-day billing cycle is used)
$1,000 + $0.74 * 30 =$1,000 + $22.20 = $1022.20

If you are unable to pay $1,000 by the end of your billing cycle, you will pay the compound interest of $22.20 in addition to the required portion of principal.

Let’s say you are unable to pay $1,000 in 30 days and only able to afford $50 this month.
(initial amount) + (interest amount per day) * ( days in a billing cycle) – (payment amount you can afford, but no less than the required minimum)
$1,000 + $0.74 * 30 – $50 = $972.20. Because of the compound interest, the initial amount decreased by only $27.80 even though you paid $50.

Let’s say, the second month you are still able to pay only $50.

Step 1: Calculate the cost of one day for a new amount to find out the cost of a new balance per day

(new outstanding balance ) * (interest rate) /365
$972.20 * 27% / 365 = $0.72 the cost of outstanding amount per day

Step 2: Calculate new interest amount

(outstanding balance) + (interest amount per day) * ( days in your billing cycle)
$972.20 + $0.72 * 30 = $993.80. This is new outstanding amount with the compound interest .

Step 3: Subtract your payment

$993.80 -$50 = $943.80

By now you should be able to see the power of compound interest. It works against you if you borrow. If you invest, the compound interest works for you.


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