This document discusses simple and compound interest concepts and examples. Simple interest is calculated by the formula A = P(1 + rt) where interest is paid once per year. Compound interest is calculated by the formula A = P(1 + r/n)^nt where interest is compounded more than once per year. The document provides examples of writing interest functions and solving for unknown variables in simple and compound interest word problems.

1. 3.5 Interest Problems

2. Simple Interest
• Simple Interest means interest is only
paid/charged to your account once per year.
A
P (1
r)
t
• A = the balance (or ending amount) after
interest is added
• P = the principle (or beginning amount)
• r = the interest rate earned/charged per year,
written as a decimal
• t = the term or time (the number of years)

3. Writing Functions
• Write a function definition for each situation:
• Principle = $158, interest rate = 3.9%
• Sara opens an account with $3210 and
earns 8% annually.

4. You Try!
• Write a function definition for each:
• Principle = $1250, interest rate = 12%
• Joe earns 2 ½ % on an initial amount of
$79.30.

5. Identifying Variables
• Identify any of the variables A, P, r, t in the
following situations:
• A = 1468(1 + 0.05)t
• 3800 = P(1.0425)5

6. You Try!
• Identify A, P, r, t :
• A = 250(1 + 0.03)t
• 2100 = P(1.123)10

7. Solving Simple Interest Problems
1. List parameters: A, P, r, t
2. Write function
3. Identify what to solve for, then solve
Example 1:
• George took out a loan for $7200, and the
bank is charging simple interest at a rate of
3.25%. How much will he owe at the end of
three years?

8. Example 2
• After 8 years, Fred owes $10000 on a loan
for which he is charged 12.5% interest.
What was his original debt?

9. You Try!
• Tom has $1500 in his account after
earning 3% interest for 7 years. How
much did he originally invest?

10. Compound Interest
• Compound Interest means interest is
added multiple times per year.
A
P 1
r
n
nt
• A = the balance (or ending amount)
• P = the principle (or beginning amount)
• r = the interest rate, written as a decimal
• n = number of times per year interest is
compounded
• t = the term (# of years)

11. Compounding Vocab
• Annually
• Semi-annually
• Quarterly
• Monthly
• Weekly
• Daily
n=1
n=2
n=4
n = 12
n = 52
n = 365

12. Example 1
• You deposit $300 in an account that pays 5%
annual interest. Find the balance after 12
years if the interest is compounded:
• Quarterly?
A=
• Monthly?
• You Try!
• Weekly?
P=
r=
n=
t=

13. Example 2
• Write a function definition for this situation:
• Taylor wants to have $10,000 after five
years with a bank account earning 6.8%
interest compounded semi-annually.
•A=
•P=
•r=
•n=
•t=

14. You Try!
• Write a function definition for this situation:
• Desmond invests $8,000 for 4 years in a
bank account earning 5 ¼ % interest
compounded monthly.
•A=
•P=
•r=
•n=
•t=

15. Example 3
• You want to have $23,000 after 4 years to
buy a car.
• Find the amount you should deposit now if
the account pays 5.9% annual interest
compounded quarterly.
•A=
•P=
•r=
•n=
•t=

16. You Try!
• New parents want to have $50,000 after 18
years for their child’s college.
• Find the amount they should deposit now if
the account pays 6.8% annual interest
compounded monthly.
•A=
•P=
•r=
•n=
•t=