Section Compound Interest. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Transcription

1 Section 11.3 Compound Interest

2 INB Table of Contents Date Topic Page # June 16, 2014 Section 11.3 Examples 32 June 16, 2014 Section 11.3 Notes

3 What You Will Learn Compound Interest Present Value 3

4 Investments An investment is the use of money or capital for income or profit. In a fixed investment, the amount invested as principal is guaranteed and the interest is computed at a fixed rate. In a variable investment, neither the principal nor the interest is guaranteed. 4

5 Compound Interest Interest that is computed on the principal and any accumulated interest is called compound interest. 5

6 Compound Interest Formula A is the amount that accumulates in the account p is the principal r is the annual interest rate as a decimal t is the time in years A p 1 r n n is the number of compound periods per year nt 6

7 Example 1: Using the Compound Interest Formula Kathy Mowers invested $3000 in a savings account with an interest rate of 1.8% compounded monthly. If Kathy makes no other deposits into this account, determine the amount in the savings account after 2 years. 7

8 Example 2: Using the Compound Interest Formula Braden River Little League receives a $50,000 donation for building a new snack bar and office building. The league decides to invest this money in a money market account that pays 4% interest compounded quarterly. How much will the league have in this account after 2 years? 10

9 Example 3: Using the Compound Interest Formula Joe Gallegos just started a new job and has received a $5000 signing bonus. Joe decides to invest this money now so that he can buy a new car in 5 years. If Joe invests in a 5-year CD paying 3.35% interest compounded quarterly, how much money will he receive from his CD in 5 years? 11

10 Annual Percent Yield The effective annual yield or annual percentage yield (APY) is the simple interest rate that gives the same amount of interest as a compound rate over the same period of time. 12

11 Example 4: Determining Effective Annual Yield Determine the effective annual yield for $1 invested for 1 year at 3.5% compounded semiannually. 13

12 Example 5: Determining Effective Annual Yield Determine the effective annual yield for $1 invested for 1 year at 4.75% compounded monthly. 14

13 Present Value Formula p p is the present value, or principal to invest now A is the amount to be accumulated in the account r is the annual interest rate as a decimal n is the number of compound periods per year t is the time in years A 1 r n nt 15

14 Example 6: Savings for College Will Hunting would like his daughter to attend college in 6 years when she finishes high school. Will would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter s college expenses. If Will estimates that he will need $30,000 in 6 years, how much should he invest now in a CD that has a rate of 2.5% compounded quarterly? 16

15 Example 7: A New Tractor Jim Roznowski wants to invest some money now to buy a new tractor in the future. If he wants to have $275,000 available in 5 years, how much does he need to invest now in a CD paying 5.15% interest compounded monthly? 18

16 Example 8: Starting a New Business Kurtis Fink's goal is to have $25,000 to start a new lawn mower repair business when he retires in 15 years. How much should Kurtis invest now in a CD that pays 2% interest compounded daily to reach his goal? 19