The document discusses simple interest calculations. It defines the principal, time, and rate factors that influence interest owed. It provides examples of calculating simple interest using the formula: Interest = Principal x Rate x Time. It also shows how to calculate the total amount owed by adding principal and interest. Step-by-step workings are shown for finding interest on loans, determining investment periods based on interest earned, and identifying interest rates based on total repayment amounts.

1. Lesson7.8: Simple Interest

2. If someone borrows money, what factors influence
how much is paid back?
Principal -How much was borrowed.
Time - How long it was borrowed for.
(in years)
Rate -
(annual % rate)
What interest was charged.
Amount to Payback = Principal + Interest
Interest = Principal  Rate  Time
I P r t
  

3. Joe borrows $200 from the bank at 6% simple
interest for 3 years. What interest does he owe,
and what is his total balance (amount to payback)
Interest Balance
I P r t
  
I  (200)(0.06)(3)
I 36

Interest owed $36

Balance = P + I
Balance = 200 + 36
Balance = 236
Balance = $236
P 200

r 6%
 0.06

t 3


4. Juan invests $5000 in bonds for 6 months at an
annual interest rate of 7%. How much interest
did he earn, and what is the balance in his account
Interest Balance
I P r t
  
I (5000)(0.07)(0.5)
I 175

Interest owed $175

Balance = P + I
Balance = 5000 + 175
Balance = 5175
Balance = $5175
P 5000

r 7%
 0.07

t 6 months
 0.5 years


5. Find the simple interest and the balance.
1) $2000 at 4% for 9 mos.
P 2000

r 4%
 0.04

t 9 mos.
 0.75 yrs.

I P r t
  
I  (2000)(0.04)(0.75)
I $60

Balance = P + I
Balance = 2000 + 60
Balance = $2060

6. Find the annual simple interest rate.
1) $2000 earns $420 simple interest over 3 years.
P 2000

I 420

t 3 years

I P r t
  
420 (2000)(r)(3)
420 6000r

Annual Interest Rate 7%

6000 6000
0.07 r


7. Find the annual simple interest rate.
2) $625 simple interest is earned on a 2 year loan
of $5000. P 5000

I 625

t 2 years

I P r t
  
625 (5000)(r)(2)
625 10,000r

r 6.25%

10,000 10,000
0.0625 r

1
or 6 %
4

8. Find the principal amount invested.
1
3) Interest of $1650 is earned over 4 years at 5 %.
2
I 1650

t 4 years

r 5.5%

I P r t
  
1650  (P)(0.055)(4)
1650 0.22P

Principal $7500

0.22 0.22
7500 P

0.055


9. Quick Draw for Points
• You will have 60 seconds to solve each
problem
• The text is Simple Interest Problems

10. To buy a car, Jessica borrowed $15,000 for 3
years at an annual simple interest rate of 9%.
How much interest will she pay if she pays the
entire loan off at the end of the third year?
Example 1: Finding Interest on a Loan
First, find the interest she will pay.
I = P  r  t Use the formula.
I = 15,000  0.09  3 Substitute. Use 0.09 for 9%.
I = 4050 Solve for I.

11. Example 1A: Finding Total Payment on a Loan
What is the total amount that she will repay?
Jessica will pay $4050 in interest.
P + I = A principal + interest = total amount
15,000 + 4050 = A Substitute.
19,050 = A Solve for A.
You can find the total amount A to be repaid on a
loan by adding the principal P to the interest I.
Jessica will repay a total of $19,050 on her loan.

12. Example 2
I = P  r  t Use the formula.
200 = 4000  0.02  t Substitute values into
the equation.
2.5 = t Solve for t.
TJ invested $4000 in a bond at a yearly rate of
2%. He earned $200 in interest. How long was
the money invested?
200 = 80t
The money was invested for 2.5 years, or 2
years and 6 months.

13. I = P  r  t Use the formula.
I = 1000  0.075  50 Substitute. Use 0.075
for 7.5%.
I = 3750 Solve for I.
The interest is $3750. Now you can find the total.
Example 3
Bertha deposited $1000 into a retirement
account when she was 18. How much will
Bertha have in this account after 50 years at a
yearly simple interest rate of 7.5%?

14. P + I = A Use the formula.
1000 + 3750 = A Substitute.
4750 = A Solve for A.
Bertha will have $4750 in the account after 50 years.
Example 3 Continued

15. Mr. Mogi borrowed $9000 for 10 years to
make home improvements. If he repaid a total
of $20,000 at what interest rate did he borrow
the money?
Example 4
P + I = A Use the formula.
9000 + I = 20,000 Substitute.
I = 20,000 – 9000 = 11,000 Subtract 9000
from both sides.
He paid $11,000 in interest. Use the amount of
interest to find the interest rate.

16. Example 4 Continued
11,000 = 90,000  r Simplify.
I = P  r  t Use the formula.
11,000 = 9000  r  10 Substitute.
11,000
90,000
= r Divide both sides by 90,000.
0.12 = r
Mr. Mogi borrowed the money at an annual rate of
about 12.2%.

17. Summary
• I = __________
• P=__________
• r = __________
• t = __________
• A=__________
• Interest Formula: I = ( )( )( )
• Amount Formula: A = ___ + ___

18. SUMMARY
Principal -How much was __________.
Time - How _____it was borrowed for.
(in_____)
Rate -
(annual % rate)
What _______was charged.
Amount to Payback = Principal + Interest
Interest = ________ ____  ______
I P r t
  