Interest calculations

Interest Calculations

Simple interest

Simple interest

An amount of money deposited into a bank for a given period of time brings to the depositor a profit called

interest.

The amount of interest I, the bank pays you, depends on the interest rate i, the amount of money deposited,

denoted as principal P also called original balance (or initial investment), and the period of time n the money

is deposited,

since P : 1 = I : (i · n) =>

Therefore,

Simple interest is calculated on a yearly basis (annually, n = 1) in which balance grows linearly with time (as

opposed to compound interest).

That is, the interest stays unchanged in each next year of saving because it is always calculated as the

percent of the same value, i.e., of the original principal P, while in the compound interest it is calculated as

the percent of the sum of the balance and the interest from the previous period.

If P is the principal or initial investment and I is the interest amount, the accumulated value at the end of n

investment periods is given by

A = P + I = P + i · P · n = P (1 + i n).

and

Example: Somebody deposits $20000 into a savings account where the rate of interest is 4.8% annually.

How much money in interest will earn after nine months?

Example: A bank lends a company money for the six months period at a rate of 8% annually.

How much was lent if the company should pay $12000 of interest?

Example: At what an interest rate was borrowed $75000 for one year if $3000 to interest is charged?

Example: For what period of time should be deposited $200000 at a 6% interest rate to earn $6000 of

interest?

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