Name:
Pre-Calculus Honors Date:
Unit 5 Lesson 8: Do Now
Solve the following equation.
Name:
Pre-Calculus Honors Date:
Unit 5 Lesson 8: Do Now
Solve the following equation.
Name:
Pre-Calculus Honors Date:
Unit 5 Lesson 8: Do Now
Solve the following equation.
Pre-Calculus Honors Date:
Book Reference 3.6
Unit 5 Lesson 8: Applications of Logarithmic and Exponential Functions
Objective:______
1. Guided Practice: Interest Compounded k times per year.
Suppose a principal P is invested at an annual interest rate r compounded k times a year for t years. Then r/k is the interest rate per compounding period and kt is the number of compounding periods. The amount A in the account after t years is
--à when interest is compounded k times per year
--à when interest is compounded continuously
Example 1: Judy has $500 to invest at 9% annual interest compounded monthly. How long will it take for the investment to grow to $3000.
Step 1: Label given information
Step 2: Plug in given information to formula
Step 3: Solve for unknown
Step 4: Write what the solution means in the context of the situation.
Example 2: Stephen has $500 to invest. What annual interest rate compounded quarterly is required to double his money in 10 years.
Step 1: Label given information
Step 2: Plug in given information to formula
Step 3: Set up window
Step 4: Graph function on graphing calculator and use trace button to find solution.
Step 5: Write what the solution means in the context of the situation.
2. Group Practice: Mathematics in Finance
1) A common basis for comparing investments is the annual percentage yield (APY)- the percentage rate that, compounded annually, will give you the same return as the given interest rate with the given compounding period.
Which investment is more attractive, an investment that pays 8.75% compounded quarterly, of another that pays 8.7% compounded monthly? Show all work and explain using the mathematics.
2) If Joelle invests $8000 into a retirement account with a 9% interest rate compounded monthly, how long will it take until this single payment has grown to $16,000?
3) What interest rate, compounded monthly, is required for an $8,500 investment to triple in 5 years?
4) The president of a bank has $18 million in his banks investment portfolio that he wants to grow to $25 million in 8 years. What is the interest rate compounded annually does he need for this investment?
Pre-Calculus Honors Homework: Pg 341-342 #(21, 23, 25, 27, 29, 41)