Unit 8, Lesson 2 Exponential Functions: Compound Interest

Do Now You have the choice of investing your money in one of two accounts. The first one has an interest rate of 5% and the interest is calculated once a year. The other account only pays 4% but the interest is calculated every 3 months. If you have $5000 to invest, which account would you chose?

Objectives & HW Be able to evaluate problems with compound interest Be able to solve problems with continuously compounded interest HW: Read p Do p. 380: 4, 64, 67, 69, 70

Review With a partner, review Lesson 1 HW Then complete the following: a)Find f(2) if f(x) = 3*2 x Ans: 3*2 2  3*4 = 12 b)Find f(3) if f(x) = e x e 3 = 19.9

Compound Interest Compound interest is calculated by using the following formula: A(t) = P(1 + r/n) nt A(t) = Amount after t years P = Principal (amount initially invested) r = interest rate (percentage) n = number of times interest is compounded each year t = number of years

Compound Interest: Example 1 If $2000 is invested in an account that earns 5% annually and is compounded quarterly, how much interest will it earn after 3 years? A(t) = P(1 + r/n) nt P = 2000; r =.05; n = 4; and t = 3 A(t) = 2000(1 +.05/4) 4*3 = 2000(1.0125) 12 = 2000(1.161) = 2322 Amount of interest is $322

Compound Interest Annually  n = 1 Semiannual  n = 2 Quarterly  n = 4 Monthly  n = 12 Daily  n = 365

Compound Interest: Example 2 How much money will need to be invested for 1 year if it is compounded monthly at 10% in order to earn at least $200? A(t) = P(1 + r/n) nt P = P(1 +.1/12) 12*1 P = P(1.0083) 12 P = P(1.104) 200 =.104P P = 200/.104 

Continuously Compounded Interest The formula for calculating continuously compounded interest is: A(t) = Pe rt Ex. What is the amount after 4 years if $5000 is invested at 6 ½ % compounded continuously? A(t) = 5000e.065(4) A(t) = 5000e.26 A(t) = 5000(1.297) A(t) = 6485