Bell Ringer

• Assume you owed someone 100% of $150. How much would you owe that person?

• If you owed someone 10% of $150, how much would you owe that person?

• Now assume, that you owed someone $150 plus 10% of $150, how much would you owe that person total?

What is interest?

An amount of money paid in addition to an original investment/loan.

OR

The amount earned or paid for the use of money.

Simple Interest and Compound Interest

It’s SIMPLE (and confounded)!

So what is the difference between simple interest and compound

interest?Simple interest is simple.

Compound interest is calculated again and again and again and again and again…………………………………………………………………………………………..and again……

If someone borrows money, what factors influenceIf someone borrows money, what factors influencehow much is paid back?how much is paid back?

Principal -Principal -How much was borrowed.How much was borrowed.Time -Time - How long it was borrowed for.How long it was borrowed for.

(in years)(in years)

RateRate -(annual % rate)(annual % rate)

What interest was charged.What interest was charged.

Amount to Payback = Principal + Interest

Interest = Principal Rate Time

I P r t

Joe borrows $200 from the bank at 6% simpleJoe borrows $200 from the bank at 6% simpleinterest for 3 years. What interest does he owe,interest for 3 years. What interest does he owe,and what is his total balance (amount to payback)?and what is his total balance (amount to payback)?

Interest Balance

I P r t I (200)(0.06)(3)

I 36

Interest owed $36

Balance = P + I

Balance = 200 + 36Balance = 236

Balance = $236

P 200r 6% 0.06t 3

Juan invests $5000 in bonds for 6 months at anJuan invests $5000 in bonds for 6 months at anannual interest rate of 7%. How much interestannual interest rate of 7%. How much interestdid he earn, and what is the balance in his account?did he earn, and what is the balance in his account?

Interest Balance

I P r t I (5000)(0.07)(0.5)

I 175

Interest owed $175

Balance = P + I

Balance = 5000 + 175Balance = 5175

Balance = $5175

P 5000r 7% 0.07t 6 months 0.5 years

Find the simple interest and the balance.Find the simple interest and the balance.

1) $2000 at 4% for 9 mos.

P 2000r 4% 0.04t 9 mos. 0.75 yrs.

I P r t I (2000)(0.04)(0.75)I $60

Balance = P + I

Balance = 2000 + 60Balance = $2060

Find the annual simple interest rate.Find the annual simple interest rate.1) $2000 earns $420 simple interest over 3 years.

P 2000I 420t 3 years

I P r t 420 (2000)(r)(3)420 6000r

Annual Interest Rate 7%

6000 60000.07 r

Now what about compound interest?

• What if we had an investment where we were paid in simple interest. Assume our investment was $1000 at 10%. How much would we have after 1 year, 2 years, 3 years, 4 years?

• After 1 year, we would have $100 earned in interest.• After 2 years, we would have $200 earned in interest.• After 3 years, we would have $300 earned in interest.• After 4 years, we would have $400 earned in interest.

But this is NOT how most investments/loans work!

How they work…

• Most investments/loans work where you earn/charged interest even on your interest and not just your original investment/loan.

So how can we account for this???

• After every year, we need to CHANGE our principal amount to our new balance. So for the second year, we would have $1,100 as our principal instead of $1,000 again.

• Let’s look at this as a table.

The TABLE using compound interest

Year Principal + Interest = Balance

1 $1,000 + $100 = $1,100

2 $1,100 + $110 = $1,210

3 $1,210 + $121 = $1,331

4 $1,331 + $133.10 = $1,464.10

But there is an easier way to compute this…

• We can also use a formula (just like we did with simple interest)

A = P (1 + r)t

A = P (1 + r)t

• A = amount we’ll end up with• P = principal• r = rate (annual interest rate as a decimal)• t = time (in years)

You try it…

• Assuming an individual invests $4,000 at 6% interest (compounded annually), what will her investment be worth in 7 years?

Homework

•Page 365#8, 9, 18, 19