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7.46.notebook
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January 13, 2020
Opening Activity:
What is 35% of $23,000?
What is 87% of $42?
$672 is 24% of what number?
If a $520 item is 30% off, how much do you take off from the price? How much do you pay for the item?
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7.4 Compound Interest
Objectives:Compute interest calculations.Apply the compound interest formula.
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If Opie invests $3500 in a bank that will give him 10% interest every year, how much money will he have at the end of the first year?
How much money will he have at the end of the second year?
How much money will he have at the end of the third year?
How much money will he have at the end of the fourth year?
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If Opie invests $3500 in a bank that will give him 10% interest every year, how much interest will they pay him at the end of the first year?
How much interest will they pay him at the end of the second year?
How much interest will they pay him at the end of the third year?
How much interest will they pay him at the end of the fourth year?
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If Opie invests $3500 in a bank that will give him 10% interest in a year, how much interest will they give him each month of that year?
What percentage does the bank use to calculate one months interest?
How many times does the bank give him interest in a year if they give him interest once per month?
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If Opie invests $3500 in a bank that will give him 10% interest in a year, but pays him interest each month, how much money will he have at the end of the first year?
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Compound Interest FormulaA = P(1 + r)t
A = final amount.P = principle.r = rate the bank gives you interest.t = number of times they give you interest.
(sometimes you need to divide the yearly rate by the number of times per year they give you interest.)
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If Opie invests $3500 in a bank that will give him 10% interest in a year, but pays him interest every 3 months (each quarter), how much money will he have at the end of the 12 years?
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Opie, Roman and Lucien just received $102,000 for their college education to put in a savings account.
Opie will go to college in 8 years, Roman will go to college in 9 years, and Lucien will go to college in 11 years.
If the savings account returns 8% interest every year, but "compounds" every 3 months, how much money will each child have in their account when the start college?
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This year, the cost of a 4year degree at MSU is $115,448.
If this amount increases by 2.9% each year, what will the cost of a 4year degree at MSU be for Opie, Roman, and Lucien when they go to college (at MSU)?
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This year, the cost of a 4year degree at MSU is $115,448.
If this amount increases by 2.9% each year, what was the cost of a 4year degree when Mr. Faber began at MSU?
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Banks are required to provide customers with an "Effective Yield" which is just the interest percent that an account will receive in one year if it compounds more than once per year.
If you invest $1 in a bank that will give you 8% interest in a year, but pays you interest every 3 months, how much money will you have at the end of the first year?
What was your "Effective Yield" or your actual interest rate for that whole year?
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Effective yield:
Y = (1 + r)t
Y = yield as a decimal.r = rate the bank gives you interest.t = number of times the bank gives you interest.
(remember, the yearly percentage rate needs to be divided by the the number of times the bank gives you interest in one year.)
The quickest and easiest way to find Effective Yield is to invest $1 for 1 year. Once you take your dollar back, what you have left is your effective yield.
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Opening Activity:Using common language, describe the pattern below.
Left Side Only: Right Side Only:500, 100, 20, 4, 0.8., 0.16,... 80, 20, 5, 1.25, 0.3125,....
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7.5 Geometric Sequences
Objectives:Describe geometric sequences recursively and explicitly.Solve real world problems with geometric sequences.
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Opie has proposed that we double his chore commission each year. Currently, we pay $0.50 per chore. When he turns 10 in August, how much will we pay him for each chore under this plan?
When he turns 11, how much will we pay him for each chore under this plan?
When he turns 16, how much will we pay him for each chore under this plan?
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We will agree to Opie's proposal that we double his chore commission each year under the condition that we reduce his current commission to $0.10 per chore.
At what age will Opie earn more than $50 per chore?
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7.6 nth Roots
Objectives:• Use nth roots to solve equations.• Represent nth roots as exponents.• Solve real world equations with exponents.
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Activity:
Left Side Only:Simplify each expression.
(x3)1/3
(y1/4)4
(z5)1/5
(q1/6)6
Right Side Only:Solve each expression.
x3 = 64
y1/3 = 4
z4 = 625
q1/4 = 5
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How many solutions (real or complex) are there to each problem?
1. x3 = 8
2. x3 = 27
3. x2 = 25
4. x2 = 16
5. x4 = 625
6. x4 = 625
Even Degree:
Odd Degree:
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Opie wants to double his chore commission every year until he is 18 years old. If he makes $0.50 per chore at age 10, what would his commission be at age 18?
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WHAT!!!!NO WAY!
The max we are willing to pay him is $3.00 per chore. Obviously we cannot multiply his chore commission by 2 each year, but what can we multiply his commission by so when he turns 18, he will earn $3.00 for each chore?
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