Simple Interest
If you have extra money you can invest it in a bank, building society or government bonds, and this investment will earn money for you at a fixed rate.
The initial sum of money you invest would be called the principal (P). The money earned on top of the principal is called interest (I) at a rate called the interest rate (r).
The simplest way of calculating interest is known as the simple interest.
If an amount $P is invested at the a rate r per annum (year) for t years, the simple interest, $I is given as follows:
I = Prt
Example 1: Calculate the simple interest when $700 is invested at a rate of 2.5% per annum for 42 months.
We first convert the number of months to years since the rate is given per annum:
40 months/12 months= 3.5 years
Then, we use the formula:
I = Prt
= $700 x (2.5/100) x 3.5
= $61.25
The simple interest is $61.25.
Compound Interest
If the interest due on savings is added to the principal at given intervals, then the interest is said to be compounded (or converted) into principal and thereafter also earns interest. As a result, the principal increases periodically and the interest compounded into the principal increases periodically throughout the term of the transaction.
The sum due at the end of the transaction is called the compound amount (A).
The difference between the compound amount and the original principal is called the compound interest (CI).
The formula for the accumulation of principal at compound interest is usually written as:
A= P(1+r)^n
A is the compound amount
n is the number of periods (usually years)
And remember, to find the compound interest:
CI= A-P
Example 2: Calculate the compound interest on $8000 if it is invested for 4 years at 8.5% per annum. (Assume that the interest is compounded yearly and at the end of each year).
We first calculate the compound amount (at the end of the period):
A= P(1+r)^n
= $8000[1 + (8.5/100)]^4
= $11086.87
Then, calculate the compound interest:
CI= A-P
= $11086.87 - $8000.00
= $3086.87