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Simple and Compound Interest

Simple and Compound Interest

Interest is defined as the cost of borrowing money, as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit, as in the case of a certificate of deposit. Interest can be calculated in two ways: simple interest or compound interest.

  • Simple interest is calculated on the principal, or original, amount of a loan.
  • Compound interest is calculated on the principal amount and the accumulated interest of previous periods, and thus can be regarded as “interest on interest.”

There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound basis rather than on a simple basis. On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation.

While simple interest and compound interest are basic financial concepts, becoming thoroughly familiar with them may help you make more informed decisions when taking out a loan or investing.

Simple Interest Formula

The formula for calculating simple interest is:

Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, then the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.

Interest on this loan is payable at $500 annually, or $1,500 over the three-year loan term.

Compound Interest Formula

The formula for calculating compound interest in a year is:

Compound Interest = total amount of principal and interest in future (or future value) less the principal amount at present, called present value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return. 

Continuing with the simple interest example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be:




While the total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into consideration the accumulated interest of previous periods. Interest payable at the end of each year is shown in the table below.

YearOpening Balance (P)Interest at 5% (I)Closing Balance (P+I)
Total Interest $1,576.25 

There are two bases on which interests are calculated:

  • Simple Interest: It is calculated on the basis of a basic amount borrowed for the entire period at a particular rate of interest. The amount borrowed is the principal for the entire period of borrowing.
  • Compound Interest: The interest of the previous year/s is/are added to the principal for the calculation of the com- pound interest.
  • Important Terminologies
  • The man who lends money is the Creditor and the man who borrows money is the Debtor.
  • The amount of money that is initially borrowed is called the Capital or Principal money.
  • The period for which money is deposited or borrowed is called Time.
  • The extra money that will be paid or received for the use of the principal after a certain period is called the Total Interest on the capital.
  • The sum of the principal and the interest at the end of any time is called the Amount.

So, Amount = Principal + Total Interest

  • Rate of Interest is the rate at which the interest is calculated and is always specified in percentage terms.

Simple Interest
I = p×t×r
P – Principal; t- time, r- rate of interest (per cent per annum)
Total Amount = I + P

Compound Interest
Let principal = P, time = t years and rate = r% per annum and let A be the total amount at the end of n years, then
A = (1+r/100)^t Read Also: Tips and Tricks: Ratio, Proportion and Variation

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