Chapter 10 Compound Interest Section 1 Introduction Compound

Chapter 10 Compound Interest

Section 1 Introduction - Compound Interest

Compound Interest ¢ …is interest computed not only on the original principle, but also on any previously credited interest.

Visual Comparison ¢ Simple Interest vs Compound Interest $10, 000 invested at 5% over 20 years.

Objective 1 Use I = PRT to compute compound interest.

Comparison using I = PRT o Invest $580 at 3% simple interest for 4 years: o Invest $580 at 3% interest compounded annually for 4 years: $580 x. 03 x 1 = $17. 40 Year 1 $580. 00 x. 03 x 1 = $17. 40 $580 x. 03 x 1 = $17. 40 Year 2 $597. 40 x. 03 x 1 = $17. 92 $580 x. 03 x 1 = $17. 40 Year 3 $615. 32 x. 03 x 1 = $18. 46 $580 x. 03 x 1 = $17. 40 Year 4 $633. 78 x. 03 x 1 = $19. 01 $69. 60 $72. 79

Compounding Period ¢ Interest can be compounded more than The compounding period defines how once a (annually). often in year one year interest is computed on an investment. Interest Compounded: Number of compounding periods in one year: annually 1 semi-annually 2 quarterly 4 monthly 12 daily 365

Practice Compound Interest using I = PRT ¢ ¢ Invest $100 at 3% interest compounded quarterly for 1 y What is the account balance at the end of the year? 1 year 1 = $0. 75 4 1 $100. 75 x 0. 03 x = $0. 76 4 $100 x 0. 03 x 1 = $0. 76 4 1 $102. 27 x 0. 03 x = $0. 77 4 $101. 51 x 0. 03 x Account Balance = $100 + $0. 75 + $0. 76 + $0. 77 = $103. 04

Limitations ¢ What if you are asked to compute this scenario? l $500 invested at 3% interest compounded monthly for 10 years? 1 = $1. 25 12 1 $501. 25 x 0. 03 x = $1. 253 12 $500 x 0. 03 x etc… You will have to do _____ 12 computations just to do the first year. You will have to do a total of 120 computations to cover _____ the full ten years.

Practice Worksheet 1 ¢ Use the Simple Interest Formula to compute compound interest. I = PRT

Compound Interest Introduction to the Compound Interest Formula M = P(1 + i) n

Compound Interest Formula Total number of compounding periods Maturity Value Principle + Interest Earned M = P(1 + i) n Interest rate per compounding period Principle: initial investment

M = P(1 + i) Compounding Period ¢ The compounding period defines how often in one year interest is computed on an investment. Interest Compounded: annually semi-annually quarterly monthly daily Number of compounding periods in one year: Interest Rate per Period (using 6% annual rate) 1 6% 2 4 6% 4 12 6% 12 365 6% 365 n

Practice Setting-up the Formula COMPOUND INTEREST FORMULA

n Practice 1 M = P(1 + i) n M = 100(1 + i) M = 100(1 +. 06) n M = 100(1 +. 06) ¢ $100 invested at 6% interest is compounded annually for 3 years. Interest rate period is: 6% 1 time(s) per year… for 3 years Interest is computed ____ 3

n Practice 2 ¢ M = P(1 + i) n M = 100(1 + . 06 2 )4 $100 invested at 6% interest is compounded semi-annually for 2 years. . 06 Interest rate period is: 6% 2 2 2 time(s) per year… for 2 years Interest is computed ____

n Practice 3 ¢ M = P(1 + i) n M = 100(1 + . 06 4 )12 $100 invested at 6% interest is compounded quarterly for 3 years. . 06 Interest rate period is: 6% 4 4 4 time(s) per year… for 3 years Interest is computed ____

n Practice 4 ¢ M = P(1 + i) n M = 100(1 + . 06 12 )60 $100 invested at 6% interest is compounded monthly for 5 years. . 06 Interest rate period is: 6% 12 12 12 time(s) per year… for 5 years Interest is computed ____

Practice Worksheet 2 ¢ Determine the interest rate period and the number of compounding periods.

Compute Compound Interest M = 100(1 +. 064 )12

Exponents M = P(1 + i) ¢ In the compound interest formula, the n value is an exponent. ¢ Exponents are short-hand notation for repeated multiplication: 6 x 6 x 6 x 6 64 n

Exponents Exponent 5 4 5 x 5 x 5 x 5 Base 4 factors Calculator Sequence: 5 4 = 625 V

Practice Use your calculator to evaluate the following: 3 ¢ 5 = 125 ¢ ¢ 7 6 4 2 = 2401 = 36

Compute w/ Calculator Practice 119. 5618171 0 M = 100(1 + 100 x . 06 4 )12 ( 1 +. 06 ÷ 4 ) $119. 56 yx 12 =

Practice Worksheet 3 ¢ Compute Compound Interest with a Calculator.

Applications Compound Interest

Example 1 of 2 M = P(1 + i). 06 4 7 yrs x 4 times/yr = 28 n 6% ÷ 4 = ¢ ¢ #16, p 408 Vickie Ewing deposits her savings of $2800 in an account paying 6% compounded quarterly and she leaves it there for 7 years. $4248. 22 l Compound Amount = ____ $1448. 22 l Interest = _____ M = 2800(1 + 2800 x . 06 28 4 ( 1 +. 06 ÷ 4 ) ) yx 28 = $4248. 22 – 2800 = $1448. 22

M = P(1 + i) Example 2 of 2 ¢ ¢ #21, p 408 $25, 000 to invest for 1 year. l l n 6% ÷ 4 =. 06 4 1 yrs x 4 times/yr = 4 Loan it out at 10% simple interest for 1 year. Invest it @6% compounded quarterly for a year. • Which option would generate the most interest, and by how much? Simple Interest I = 25, 000(0. 10)(1) $2500 – 1534. 09 = $965. 91 Compound Interest. 06 4 4 M = 25, 000(1 + ) M = $26, 534. 09 I = $26, 534. 09 – 25, 000 $1534. 09

Practice ¢ Ch 10, Section 1 – Compound Interest Textbook Exercise 10. 1 (pages 407 – 410) _____ #2, 3, 6, 7, 9, 16, 17, 19, 21, 23, 25 NOTE: Use the M = P(1 + i)n formula for all the problems where you are to compute compound interest. Because we are using the formula to determine M (as opposed to using a table), our answers may be just a bit different from the book’s answer key.