Simple Interest
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Transcript of Simple Interest
![Page 1: Simple Interest](https://reader035.fdocuments.us/reader035/viewer/2022062307/556824e9d8b42ab7198b459f/html5/thumbnails/1.jpg)
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?
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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.
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Simple Interest and Compound Interest
It’s SIMPLE (and confounded)!
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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……
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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
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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
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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
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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
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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
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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.
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But this is NOT how most investments/loans work!
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How they work…
• Most investments/loans work where you earn/charged interest even on your interest and not just your original investment/loan.
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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.
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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
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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
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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)
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You try it…
• Assuming an individual invests $4,000 at 6% interest (compounded annually), what will her investment be worth in 7 years?
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Homework
•Page 365#8, 9, 18, 19