INTEREST

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Simple Interest

Example 1 | Example 2
 
The amount of simple interest is determined by the formula I = Prt
where:
I is the amount of interest earned (in dollars)
P is the principal sum of money earning interest (in dollars)
r is the annual interest rate (a decimal)
t is the time period (in years)
Examples:
1. Ross just sold his old computer for $750 and had decided to put the money in a bank that is paying 9.25% interest. If he leaves his money for 4 years how much interest will he have made?

2. 250 days ago, Olga invested some money that she has been saving for a trip to Columbia. If she earned $256.25 in interest at a rate of 10.25 %, how much money did she originally invest?
a) Manipulate the simple interest formula to solve for P
I=Prt   -------> P

 =

 _I_
     

 rt
b) Convert r to a decimal
10.25% ------> 0.1025
c) Convert t into years
250 Days  -------> 250
    365
d) Use your formula to solve for P
     P =

    _I_
       

    rt
     P =

    _($ 256.25)_
       

    (0.0125) (250)

       

    (365 )

    P =$ 3650.00
Olga originally invested $3650.00
 
Mini Lessons
 
Compound Interest
 
Example 1 | Example 2
 
The amount of compound interest is determined by the formula
 A = P(1 + i) n
Where:
A is the accumulated value (in dollars)
P is the principal (in dollars)
i is the periodic interest rate (a decimal)
n is the number of compounding periods
Examples:
1. Rebecca is a seamstress who just opened her first shop. She has decided to invest her first $2000 in an account for her retirement where interest is compounded annually at 10.5%. If Rebecca plans to work for 35 years, how much money will she have in that account when she retires?
a) Convert r to a decimal
10.5% ------> 0.105
b) Use the formula to solve for A
A = P(1 + i) n
A = $2000(1 + 0.105) 35
A = $2000(1.105) 35
A = $2000(32.9367)
A = $65 873.35
When Rebecca retires in 35 years, she will have $65 873.35 in her account.

2. Keith wants to buy a grand piano when he finishes his masters degree in 3 years. He has found a bank that will give him an interest rate of 12% compounded annually. If he will need $15 000 for the piano, how much does he need to invest now?
a) Convert r to a decimal
12% ------> 0.12
b) Change the formula to solve for P
A = P(1 + i) n
P
=

____A___ (1 + i ) n

c) Solve the equation for P
P
=

_$15 000 (1+0.12) 3
P
=

_$15 000 (1.12 ) 3
P
=

$15 000 1.4049
P
= $ 10 0676.70

Keith will need to invest $ 10 0676.70 now if he wants to have $15 000 in 3 years.
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