Lesson 7.8: Simple Lesson 7.8: Simple InterestInterest

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 TimeI 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 BalanceI P r t I (200)(0.06)(3)I 36

Interest owed $36

Balance = P + IBalance = 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 BalanceI P r t I (5000)(0.07)(0.5)I 175

Interest owed $175

Balance = P + IBalance = 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 + IBalance = 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

Find the annual simple interest rate.Find the annual simple interest rate.2) $625 simple interest is earned on a 2 year loan of $5000. P 5000

I 625t 2 years

I P r t 625 (5000)(r)(2)625 10,000r

r 6.25%

10,000 10,0000.0625 r

1or 6 %4

Find the principal amount invested.Find the principal amount invested.13) Interest of $1650 is earned over 4 years at 5 %.2

I 1650t 4 yearsr 5.5%

I P r t 1650 (P)(0.055)(4)1650 0.22P

Principal $7500

0.22 0.227500 P

0.055

Quick Draw for Points

• You will have 60 seconds to solve each problem

• The text is Simple Interest Problems

To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year?

Example 1: Finding Interest on a Loan

First, find the interest she will pay.I = P r t Use the formula.I = 15,000 0.09 3 Substitute. Use 0.09 for 9%.

I = 4050 Solve for I.

Example 1A: Finding Total Payment on a Loan

What is the total amount that she will repay?

Jessica will pay $4050 in interest.

P + I = A principal + interest = total amount15,000 + 4050 = A Substitute.

19,050 = A Solve for A.

You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.

Jessica will repay a total of $19,050 on her loan.

Example 2

I = P r t Use the formula.

200 = 4000 0.02 t Substitute values into the equation.

2.5 = t Solve for t.

TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested?

200 = 80t

The money was invested for 2.5 years, or 2 years and 6 months.

I = P r t Use the formula.

I = 1000 0.075 50 Substitute. Use 0.075 for 7.5%.

I = 3750 Solve for I.

The interest is $3750. Now you can find the total.

Example 3Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%?

P + I = A Use the formula.

1000 + 3750 = A Substitute.

4750 = A Solve for A.

Bertha will have $4750 in the account after 50 years.

Example 3 Continued

Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money?

Example 4

P + I = A Use the formula.9000 + I = 20,000 Substitute.

I = 20,000 – 9000 = 11,000 Subtract 9000 from both sides.

He paid $11,000 in interest. Use the amount of interest to find the interest rate.

Example 4 Continued

11,000 = 90,000 r Simplify.

I = P r t Use the formula.11,000 = 9000 r 10 Substitute.

11,000 90,000 = r Divide both sides by 90,000.

0.12 = r

Mr. Mogi borrowed the money at an annual rate of about 12.2%.

Summary

• I = __________• P=__________• r = __________• t = __________• A=__________

• Interest Formula: I = ( )( )( )• Amount Formula: A = ___ + ___

SUMMARYSUMMARY

Principal -Principal -How much was __________.How much was __________.Time -Time - How _____it was borrowed for.How _____it was borrowed for.

(in_____)(in_____)RateRate -

(annual % rate)(annual % rate)What _______was charged.What _______was charged.

Amount to Payback = Principal + Interest

Interest = ____________ ______I P r t