simple & compound interest. objective: 7.1.01 develop and use ratios, proportions, and percents...
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Simple & Compound Interest
Simple & Compound InterestObjective:7.1.01 Develop and use ratios, proportions, and
percents to solve problems
Essential Question: How can I use percents to calculate simple and compound interest?
Vocabulary:Interest: an specified amount of money paid or earned for the
use of money.Principal: the original amount of money borrowed or deposited.Rate: the interest percentage.Time: the period of time for which an amount of money is
invested or borrowed.Simple Interest: an interest calculation that is calculated only
on the principal.Compound Interest: an interest calculation that is calculated
using the principal and any interest remaining in an account.
Simple & Compound Interest
Real World Example:Simon is 12 years old and has decided that he wants to buy a car when he turns 16. He has some money and thinks if he puts it in the bank for the next four years he will get enough interest to buy a car. If he invests $3000 and receives 4% simple interest over the next four years, how much will he have to spend on a new car?
Simple & Compound Interest
Simon will have a total of $3,480 to
spend on a car when he turns 16
I = PrtI = (3000)(0.04)(4)
I = $480
Simple Interest Formula
Simple & Compound Interest
I = PrtInterest
Principal
Rate
Time (in years)
Compound Interest Formula
Simple & Compound Interest
B = P(1 + )nt
Balance
Principal Rate
Time (in years)
rn
Simple & Compound InterestExample 1: Finding Simple InterestFind the simple interest for $4,000 invested for 4 years at an annual interest rate of 4%.
$4,640.00
I = PrtI =
P = r = t =
?4,0004% = 0.044 years
I = (4000)(0.04)(4)
I = $640$4,000 + $640
Simple & Compound InterestExample 2: Finding Compound InterestIf you deposit $4,000 in an account that pays 4% compounded annually what is your balance after 4 years.
$4,679.43
B = p(1 + r)t
B = p = r = t =
?4,0004% = 0.044 years
B = 4000(1 + 0.04)4
B = $4679.43
Simple & Compound InterestExample 3: Finding Simple InterestFind the simple interest for $2,500 invested for 4½ years at an interest rate of 4.5%.
$3,006.25
I = PrtI =
P = r = t =
?2,5004.5% = 0.0454.5
I = (2500)(0.045)(4.5)
I = $506.25$2,500 + $506.25
Simple & Compound InterestExample 4: Finding Simple InterestFind the simple interest for $80 invested for 6 months earning 6% simple interest.
$82.40
I = PrtI =
P = r = t =
?806% = 0.066/12 = 0.5
I = (80)(0.06)(6/12)
I = $2.40$80.00 + $2.40
Simple & Compound InterestExample 5: Using Simple Interest to Find TimeIf you invest $8,000 and receive 9% simple interest, how long would it take to earn $5,040 in interest.
t = 7 years
I = PrtI =
P = r = t =
5,0408,0009% = 0.09?
5040 = (8000)(0.09)(t)
5040 = 720t720 720
Simple & Compound InterestExample 6: Using Simple Interest to Find RateIf you invest $8,000 and receive $5040 in simple interest after 7 years, what was the interest rate.
r = 0.09
I = PrtI =
P = r = t =
5,0408,000?7
5040 = (8000)(r)(7)
5040 = 56000r56000 56000
When Calculating Interest:Simple & Compound Interest
Always Remember…First make sure you are using the correct formula…is it simple interest or compound interest?
Make the correct substitutions…p is principal, r is interest rate, t is time in years, and B is balance.
Solve for the unknown.
Reread the question and calculate your answer.
Independent Practice:Find the interest for each example below:
1. $800, 5 years, 5% interest
2. $1,500, 6½ years, 8% interest
3. $450, 7 years, 11.75% interest
Simple & Compound Interest
= $200.00
= $780.00= $370.13
Independent Practice:Find the interest for each example below:
1. $800, 5 years, 5% interest
2. $1,500, 6½ years, 8% interest
3. $450, 7 years, 11.75% interest
Simple & Compound Interest
= $200.00
= $780.00= $370.13
HOMEWORK
Simple & Compound Interest