lesson 7.8: simple interest. if someone borrows money, what factors influence how much is paid back?...
TRANSCRIPT
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
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 amount
15,000 + 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 3
Bertha 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