Simple and Compound Interest

Simple- interest that gets calculated a grand total of one time

compound- interest is calculated continuely at the end of every compounding period

Interest:
(think 2 perspectives)
* lend .......... * borrow.
(invest) .......
*to bank ..... *from bank
give ......... get

An amount of money generated through the use of 3 variables:
PRINCIPAL AMOUNT(P)$
INTEREST RATE (r)%
TIME (t)years

SIMPLE
I=(P)(r)(t)

COMPOUND
A=1(P+r/n)n(t)

P=principal
r=rate
t=time
n=number of compoundings per year
I=interest (by itself)
A=amount(principal plus interest)




Example

Bob invests money. He starts with $1000.00. He invests it at 5% interest. He invests only 1 year at a time, but every year he decides to reinvest his interest. Calculate the value of his investment at the endof 5 years.

^^ simple interest(5 times).
I=Prt

I=?
P=1000
r=0.05
t=1

1.....I=Prt
=(1000)(0.05)(1)
=$50
at end of 1st year, he earns $50.

2.....
I=Prt
=(1050)(0.05)(1)
=$52.50

3.....
I=Prt
=(1102.50)(0.05)(1)
$=55.13

4.....
I=Prt
=(1157.63)(0.05)(1)
=$57.88

5.....
I=Prt
=(1215.51)(0.05)(1)
=$60.78

Total value of his investment:
$1276.29
^^ this is the compounded amount
(interest was added.. (compounded)
to the principal each time).

OR ..
once through this formula.

A=P(1+r/n)n(t)
A=1000(1+0.05/1)(1)(5)
A=1000(1.05)^5
A=1276.28

Hmmmm.... remember this ..
y=a*b^x