Simple and
compound
interests
Rahma Taha
Some relevant terms:
Principal: amount your
account starts with. This
could be a starting
investment, or the starting
amount of a loan
Interest: a percent of the
principal.
Simple
interest:
●
Simple interest is a
percentage of the
principal added to the
loan amount regularly,
such as by month,
quarter or year.
●
It can be expressed as a
formula : P x R x T
●
●
●
●
Where:
P =Principal
R =Interest rate
T =Term of the loan
Example (1):
You borrow $5,000 to be repaid over five years. The bank
charges you a simple interest rate of 2.8%. It’s a fixed
percentage that won’t change. Using the formula I = p x r x
t formula to calculate the total amount of simple interest
you owe: 5,000 x .0.28 x 5, which comes to $700. You will
pay a total of $700 in simple interest over five years.
Example (2):
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:
●
●
●
●
●
Compound interest is when you
add the earned interest back
into your principal balance,
which then earns you even
more interest, compounding
your returns.
It can be expressed as a
formula : P (1 + [r / n]) ^
nt
Where:
P = the principal amount r =
the annual rate of interest
(as a decimal)
n = the number of times the
interest is compounded per
year
t = the number of years
(time) the amount is
deposited for
Example (1):
Let’s say you put $5,000 into a savings account paying 5%
interest. The account is compounded monthly for 10 years.
In this situation, you know P ($5,000), r (.05), n (12),
and t (10). Now, let’s put those in the compound interest
formula.
A
A
A
A
A
=
=
=
=
=
P (1 + [r / n]) ^ nt
5,000 (1 + [.05 / 12]) ^ (12 * 10)
5,000 (1.00417) ^ (120)
5,000 (1.64767)
8,238.35
Life application
Consumer
(and Other)
Loans
Car loans
Certificates
of Deposits
Discounts
on Early
Payments
Simple interest
Compound interest
Can be defined as the interest
charged on the total principal
amount taken for a particular
period of time.
Calculated on the revised principal.
The revised principal is calculated
based on the interest charged on
the accrued interest. The principal
amount, therefore, keeps on
increasing.
Smaller
Larger
Formula : P x R x T
Formula : P (1 + [r / n]) ^ nt
Principal and interest growth is
constant
Principal and interest growth is
rapid and increases at a fast pace
The simple interest offers low
returns for the lender
The compound interest offers a
high return to the lenders
Extra
info
Compound Annual Growth
Rate (CAGR)
-The compound annual growth rate isn’t a
true return rate, but rather a
representational figure. It is essentially
a number that describes the rate at which
an investment would have grown if it had
grown at the same rate every year and the
profits were reinvested at the end of each
year.
Rule of 72
-The Rule of 72 is a quick, useful formula
that is popularly used to estimate the
number of years required to double the
invested money at a given annual rate of
return.
For example, if an investment scheme
promises an 8% annual compounded rate of
return, it will take approximately nine
years (72 / 8 = 9) to double the invested
money. Note that a compound annual return
of 8% is plugged into this equation as 8,
and not 0.08, giving a result of nine
years (and not 900).