Growth Models
Interest Calculations
Budgets
Taxes
Inflation and CPI
100
Describe the difference between a linear growth model and an exponential growth model.
A Linear model grows by a constant value (number) while an Exponential model grows by a constant rate (percentage).
100
The the total interest that will be paid in one year is called what?
APR or Annual Percentage Rate
100
In a 50/30/20 budget, how much should you put aside for savings?
20%
100
If the total withholdings on your W-2 exceed your total taxes owed, what will happen when you file?
You'll get a refund.
100
What does CPI stand for?
Consumer Price Index
200
3-year old Carmen has $40 in her piggy bank right now. If her aunt will give her $25 each year for her birthday, write an explicit equation and determine how much she'll have when she is 16.
Pn=40+25*n
P13=40+25*13=$365
200
Alexa invests $2000 in a simple interest savings account that earns 8% APR. How much will she have after 5 years?
$2800
A=P0*(1+rt)=2000*(1+0.08*5)=2800
200
The difference between gross and net income is what?
Gross income is your total earned wages. Net income is what your paycheck includes (after deductions, taxes, etc.).
200
Looking at the image below, what is the total federal taxes withheld?
$6,835
200
A gallon of milk costs $2.30 today. If the inflation rate is 3.9%, what will the cost be in 26 years if the rate is constant?
$6.34
FV=Pert=2.3*e0.039*26
300
Elgin's population in 2022 was 113,177. If the city's population is growing by a constant 1.52% each year, what should we expect the population to be this year?
116,644 people
Pn=(1+r)n∗P0
=(1+0.0152)2*113177=116643.73
300
Alexa invests $2000 in a compound interest savings account that earns 8% APR. If interest is compounded quarterly, how much interest will she earn over 10 years?
$2416.08
Pn=P0∗(1+ r/k)Nk=2000*(1+0.08/4)10*4=4416.08
I=Pn-P0=4416.08-2000=2416.08
300
Alicia makes a salary of $2300 per month and she also earns an annual bonus of $250 paid out monthly. If her monthly expenses are $2107, what is her monthly cash flow (leftover)?
$213.83
300
Anthony earned $80,000 last year. He made a $4,000 pre-tax deposit to his retirement account, and took the $6100 standard deduction, plus 2 exemptions ($3900 each) for himself and his son. What is Anthony's taxable income?
$62,100
300
The price of a candy bar in 2021 was $2.50 and can be determined using the equation y=2.5(1+r)t. If the cost of the candy in 2023 was 2.86, what is the inflation rate?
6.96%
2.86=2.5(1+r)2=0.0696
400
Leila's company increases salaries by 5.43% each year. If her current salary is $42,000, write an explicit equation to model her salary growth.
Pn=42000*(1+0.543)n
400
Juan takes out a 30-year mortgage for $250,000 at 8% interest compounded monthly. Calculate his monthly payment.
$1,834.41
(use the TVM Calculator to solve for payments)
400
Last month, Hannah spent $965 on rent, $25 on her water bill, $155 on her electric bill, $84 on the gas bill, $215 on groceries, $134 on her student loan payment, $200 for her church's tithe, and $56 on her internet/phone bill. If this month's expenses will be the same, what is the minimum income Hannah will need to make AND what percent of her income will be spent on housing?
Income = $1834
Housing = 52.6%
400
Marco buys lunch at Texas Roadhouse for $19.99. Tax on his meal is 8.29% and he plans to tip the waitress 20%. How much will he pay in total?
$25.98
Tax=19.99*0.0829=1.66
Tip=(19.99+1.66)*0.2=4.33
400
If the CPI in 2000 was 172.2 and the CPI in 2012 was 229.6, calculate the inflation rate.
33.33%
I=(CPIe-CPIs)/CPIs
500
Scientists are studying a new virus. At the beginning of the experiment, their petri dish contains 250 infected cells. After 5 hours, there are 1500 infected cells. How long will it take for the number of infected cells to reach 2000?
5.81 hours
Pn=P0*(1+r)n
1500=250*(1+r)5 --> r=0.43
2000=250*(1+0.43)n --> n=5.81
500
How much money will you need in your retirement account if you plan to take out payments of $2500 each month for 25 years after you retire and your account earns 12% interest compounded semi-annually?
$242,271.64
(use the TVM Calculator to solve for present value -- use the "advanced" version, since the payments are monthly and the interest is semi-annual)
500
Launa and Jack are planning a 3-day romantic getaway. If the average cost of hotel stay per night is $105 plus 18% hotel tax, determine the total cost for hotels for their trip.
$247.8
Cost=105*2+(105*2)*0.18=247.8
500
John got $20 for his birthday yesterday. If he spends it on lunch, what can he spend on the meal if he knows he has to pay 5.5% in taxes?
$18.96
Total = Meal + (Meal*0.055)
500
If the cost of a gallon of gas in 1990 was $1.80, what is that in terms of 2010 dollars?
| Year | CPI |
|---|---|
| 1990 | 130.7 |
| 2000 | 172.2 |
| 2010 | 218.1 |
| 2020 | 258.8 |
$3.00
V=P*CPIe/CPIs=1.8*(218.1/130.7)=3.0036