11.8 Compound interest and half life.notebook November 08, 2017 Compound Interest AND Half­ Lives Nov 2­1:43 PM What is compound interest?? This is when a bank pays interest on both the principal amount AND on accrued interest. **This is different from simple interest....how is that? • Simple interest is interest earned solely on the principal amount. • Remember I=prt?? Nov 2­1:43 PM 1 11.8 Compound interest and half life.notebook November 08, 2017 Let's take a look at a chart when interest is compound at an annual rate of 8% Interest Rate Time Periods in a Earned Per Compounded Year Period annually 1 8% per year 8% / 2 periods so..... semi­annually 2 4% every 6 months 8% / 4 periods so...... quarterly 4 2% every 3 months 8% / 12 periods so..... monthly 12 0.6% every month Nov 2­1:47 PM How do we find compound interest? Nov 2­1:53 PM 2 11.8 Compound interest and half life.notebook November 08, 2017 $1,500 at 7% compounded annually for 3 years Nov 2­2:08 PM Suppose your parents deposited $1500 in an account paying 6.5% interest compounded quarterly when you were born. Find the account balance after 18 years. Nov 3­8:29 AM 3 11.8 Compound interest and half life.notebook November 08, 2017 You deposit $200 into a savings account earning 5% compounded semi­annually. How much will it be worth after 1 year? After 2 years? After 5 years? Nov 3­8:29 AM What is a half­life? A half­life is the length of time it takes for one half of the substance to decay into another substance. Nov 2­2:09 PM 4 11.8 Compound interest and half life.notebook November 08, 2017 We will use the exponential function model to determine half lives: a = your initial amount (what you start with) b = always 0.5 or 1/2 to represent the half life (REMEMBER ­ b is always the growth or decay factor ­ in this case DECAY) x = the number of times your half life occurs Nov 2­2:10 PM The half­life of iodine­124 is 4 days. A technician measures a 40­mCi sample of iodine­124. a. How many half­lives occur in 16 days? b. How much iodine­124 is left in the sample after 16 days? Nov 3­8:30 AM 5 11.8 Compound interest and half life.notebook November 08, 2017 The half­life of carbon­11 is 20 minutes. A sample of carbon­11 has 25 mCi. a. How many half­lives occur in 1 hour? b. How much carbon­11 is left in the sample after 1 hour? Nov 3­8:34 AM A patient is given 30 grams of iodine­131. A half­life for this substance is 8 days. How much of the substance remains in their system a. after 8 days? b. after 16 days? Nov 2­2:14 PM 6.