Simple interest vs compound interest

Businesses invest the surplus amounts to earn a profit on it. The simplest investment is putting the surplus in the bank which provides interest on that amount. There are two types of interest:

1. Simple Interest
2. Compound Interest

Let’s see the details of simple interest vs compound interest.

Simple Interest – Definition

It is the interest that is calculated on the principal amount without taking into account the interest received.

Formula

Future Value = P + (P x r x n)

Where,

P = Principal Amount (Amount that is invested)

r = Rate of Interest in decimals

n = time period in years

Explanation

Let us take the example of Mr. Ali. He has \$500 and he wants to invest it in the bank. The bank has a simple interest rate of 10%. Mr. Ali wants to invest this amount for 2 years. The interest he would receive on this amount per year would be \$50 (\$500 *10%). For two years, the total interest would amount to \$100. Thus, after the end of 2 years, Mr. Ali’s \$500 would increase to \$600 i.e., \$500 (principal) + \$100 (two years’ interest). This can also be calculated using the above formula as follows:

Future Value = P + (P x r x n)

Future Value = 500 + (500 x 0.1 x 2)

Future Value = 500 + 100

Future Value = \$600

Example – Simple Interest

A business has a \$30,000 surplus. Management knows that this would not be needed for at least 6 months so they want to invest it to earn interest. The bank has provided them with an interest rate of 8%. How much interest can the business earn and what will be the future value of this amount after 6 months?

Solution

Future Value = P + (P x r x n)

Future Value = 30,000 + (30,000 x 0.08 x 6/12)

Future Value = 30,000 + 1,200

Future Value = \$31,200

Thus, the business can earn an interest of \$1,200 in 6 months at an interest rate of 8% and this would increase the principal amount to \$31,200

Compound Interest – Definition

It is the method of calculating the future value of the investment after taking into account the interest earned on that investment.

Formula

Future Value = P(1+r)n

Explanation

Let us take the example of Brix Limited. The company has a surplus of \$25,000 which the management has estimated will not be useful for 3 years. Management wants to invest this amount into a bank with an interest rate of 12%. The interest earned will be added and interest will be calculated on the total amount. Thus, the interest of \$3,000 (\$25,000 * 12%) will be earned in the first year. The total amount at the end of the first year would be \$28,000 (\$25,000 + \$3,000). The interest for the second year will be calculated on this sum and will amount to \$3,360 (\$28,000 * 12%). This will increase the total amount at the end of the second year to \$31,360. The interest of the third year will be calculated on this amount. Thus, the interest of \$3,763.2 (\$31,360*12%) will be earned in the third year. The amount at the end of the third year will be \$35,123.2. This is the future value of \$25,000 that is invested at the rate of 12% for 3 years on a compounding basis. The total interest earned is \$10,123.2 (\$3,000 + \$3,360 + \$3,763.2).

There is another method to calculate this future value using the formula as follows:

Future Value = P(1+r)n

Future Value = 25,000 x (1+0.12)3

Future Value = \$35,123.2

Interest Earned = \$35,123.2 – \$25,000

Interest Earned = \$10,123.2

Example – Compound interest

\$7,000 is invested in the bank account with an interest rate of 9% for 6 years. What is the future value of the investment and the interest earned?

Solution

Future Value = P(1+r)n

Future Value = 7,000 x (1+0.09)6

Future Value = \$11,740

Interest Earned = \$11,470 – \$7,000

Interest Earned = \$4,470

Nominal interest vs Effective Interest

The Nominal Interest rate is the rate that is given for a period. The effective Interest rate is calculated after compounding the nominal interest rate. It is the interest rate that has the same effect as a nominal interest rate compounded for several periods.

Formula of effective interest rate

Effective Interest Rate = (1+i/n)n – 1

Where,

i =  Nominal Interest Rate

n = number of compounding periods

Example

A company wants to invest at the rate of 12% per month for a whole year. What is the effective annual rate?

Solution

Effective Interest Rate = (1+i/n)n – 1

Effective Interest Rate = (1+0.12/12)12 – 1

Effective Interest Rate = 12.68%