11.8 Compound and half life.notebook November 08, 2017

Compound Interest AND Half­ Lives

Nov 2­1:43 PM

What is ??

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 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