Question

Explain the concept of compounded interest, and how this compounding may benefit one’s retirement savings. For example, (not that any of us will receive a 100% interest compound on a daily basis), but imagine you began with a single penny. If you were able to compound and double your investment each day, how much would you have accumulated in a mere 30-day period? The answer is amazing … at $5,368,709.12. Share examples your explanation of compounding interest.

Answer 1

Concept of Compound Interest

Compound interest refers to increase in the principal amount with the interest earned on the previous amount. In simple terms, it means interest on interest. Let us try to understand it with the help of an example.

Suppose you deposit $1000 in your bank account today and the bank offers interest rate that is compounded annually @ 5%. What will be the amount in the bank after 3 years?

For the 1st year :

Interest will be 1000*5/100 = $50, now this interest will be added back to the principal amount for the next year.

For the 2nd year :

The principal amount is 1000 + the interest of $50. This make total amount on which 5% will be provided as $1050.

Interest will be 1050*5/100 = 52.55. This shall be added back to the total amount next year.

For the 3rd year:

The principal amount is 1050+52.55 = 1102.55

Interest will be 1102.55*5/100 = 55.1275

So the total amount after 3 years will be 1102.55 + 55.1275 = $1157.67

Compounding for year 1 = 1000(1.05)

Compounding for year 2 = 1000(1.05)(1.05)

Compounding for year 3 = 1000(1.05)^3

Compounding for n years at rate R with principal P = P(1 + R)^n

Benefits of Compounding interest over simple interest

Simple interest does not add back the interest earned on the previous amount. This reduces the earning potential of an investor. Lets take the same example but this time the amount bears simple interest.

Interest for 3 year period = (1000*5/100)*3 = $150.

Notice that the principal amount on which interest is provided remains same in all the 3 years. Hence total earning from simple interest rate is $1150 which is less than compound interest amount by $7.67.

This is the beauty of compounding. In long run this difference of $7.67 becomes huge as there is interest on this amount and interest earned on this also bears interest and so on. This is a classic example to understand compound interest.