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MTH 216 Week 5 Study Plan for Final Examination

1.C Sets and Venn Diagrams

• Use Venn diagrams with three sets.

• 4.A Taking Control of Your Finances

• Calculate net cash flow.
• Analyze spending patterns and options.
• Solve application problems involving expenses.

• 4.B The Power of Compounding

• Calculate simple and compound interest.
• Find the annual percentage yield (APY).
• Calculate continuous compound interest.

• 4.C Savings Plans and Investments

• Decide if a statement involving savings plans and investments makes sense.
• Calculate and interpret balances using the savings plan formula.
• Calculate total and annual returns.

• 4.D Loan Payments, Credit Cards, and Mortgages

• Calculate loan payments, total payments, and total interest and principal.
• Analyze credit card debt.
• Analyze loan options, mortgage options, and closing costs.

• 4.E Income Taxes

• Calculate gross income, adjusted gross income, and taxable income.
• Compute FICA taxes and total tax bills.
• Calculate tax credits and deductions.
• Determine whether renting or buying is cheaper.

• 6.B Measures of Variation

• Find the standard deviation and five-number summary for a data set.

• 7.B Combining Probabilities

• Solve probability problems.

MTH 216 Week 5 Checkpoint

Compute the total cost per year of the following pair of expenses. Then complete the​ sentence: On an annual​ basis, the first set of expenses is​ _______% of the second set of expenses.

Maria spends ​$15

on lottery tickets every week and spends ​$139

per month on food.

On an annual​ basis, the money spent on lottery tickets is 47

​%

of the money spent to buy food.

Consider a relatively simple health insurance plan with the following provisions. Office visits require a​ co-payment of ​$25

.

Emergency room visits have a ​$250

​co-payment. Surgical operations have a ​$1 comma 700

deductible​ (the first ​$1 comma 700

is paid out of​ pocket). The monthly premium is ​$360

.

During a​ one-year period, somebody insured by this health insurance has the expenses shown to the right. Complete parts​ (a) and​ (b) below.

Expenses

Total Cost

Feb.​ 18: Office visit

​$150

Mar.​ 26:Emergency room

​$720

Apr.​ 23: Office visit

​$150

May​ 14: Surgery

​$6 comma 500

July​ 1: Office visit

​$150

Sept.​ 23: Emergency room

​$950

1. Determine the​ person’s health care expenses for the year with the insurance policy.

The​ person’s health care expenses with the insurance policy are ​$6595

.

​(Type a whole​ number.)

1. Determine the​ person’s health care expenses for the year without the insurance policy.

The​ person’s health care expenses without the insurance policy are ​$8620

.

Calculate the amount of money​ you’ll have at the end of the indicated time period.

You invest ​$1000

in an account that pays simple interest of 7

​%

for 20

years.

The amount of money​ you’ll have at the end of 20

years is ​$2400

.

Find the annual percentage yield​ (APY) in the following situation.

A bank offers an APR of 6.6

​%

compounded daily.

The annual percentage yield is 6.82

​%.

Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account.

A ​$17 comma 000

deposit in an account with an APR of 4.75

​%.

The balance in the account after 1

year is approximately ​$17826.99

.

​(Round to the nearest cent as​ needed.)

The balance in the account after 5

years is approximately ​$21557.27

.

​(Round to the nearest cent as​ needed.)

The balance in the account after 20

years is approximately ​$43957.06

.

​(Round to the nearest cent as​ needed.)

The APY for the account is approximately 4.86

​%

Use the savings plan formula to answer the following question.

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6 %

.

How much should you deposit monthly to accumulate ​$83 comma 000

in 13

​years?

You should invest ​$352.52

each month.

Compute the total and annual returns on the described investment.

Six

years after buying 50

shares of XYZ stock for ​$40

per​ share, you sell the stock for $ 2900.

The total return is 45

​%.

​(Do not round until the final answer. Then round to one decimal place as​ needed.)

The annual return is 6.4

​%.

​(Do not round until the final answer. Then round to one decimal place as​ needed.)

Consider a home mortgage of ​$200 comma 000

at a fixed APR of 6

​%

for 20

years.

1. Calculate the monthly payment.
2. Determine the total amount paid over the term of the loan.
3. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
4. The monthly payment is ​$1432.86

.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

343886. The total amount paid over the term of the loan is ​$343886.4

.

​(Round to the nearest cent as​ needed.)

58. Of the total amount​ paid, 58.2

​%

is paid toward the​ principal, and 41.8

​%

is paid for interest.

​(Round to one decimal place as​ needed.)

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$140 comma 000

loan.

Option​ 1: a​ 30-year loan at an APR of 7

​%.

Option​ 2: a​ 15-year loan at an APR of 6.5

​%.

Find the monthly payment for each option.

The monthly payment for option 1 is ​$931.42

.

The monthly payment for option 2 is ​$1219.55

.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Find the total amount paid for each option.

The total payment for option 1 is ​$335311.2

.

The total payment for option 2 is ​$219519

.

​(Use the answers from the previous step to find this answer. Round to the nearest cent as​ needed.)

Compare the two options. Which appears to be the better​ option?

A.

Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B.

Option 2 will always be the better option

C.

Option 1 will always be the better option.

D.

Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

A man

earned wages of ​$41 comma 700

​,

received ​$1700

in interest from a savings​ account, and contributed ​$3400

to a​ tax-deferred retirement plan. He

was entitled to a personal exemption of ​$2700

and had deductions totaling ​$5470

.

Find his

gross​ income, adjusted gross​ income, and taxable income.

His

gross income was ​$43400

.

​(Simplify your​ answer.)

His

adjusted gross income was ​$40000

.

​(Simplify your​ answer.)

His

taxable income was ​$31830

.

​(Simplify your​ answer.)

Use the marginal tax rates in the table below to compute the tax owed in the following situation.

Marco

is married filing separately

with

a taxable income of ​$67 comma 600

.

Tax Rate

Single

Married Filing Separately

​10%

up to​ $8,925

up to​ $8,925

​15%

up to​ $36,250

up to​ $36,250

​25%

up to​ $87,850

up to​ $73,200

​28%

up to​ $183,250

up to​ $111,525

​33%

up to​ $398,350

up to​ $199,175

​35%

up to​ $400,000

up to​ $400,000

standard deduction

​$6100

​$6100

exemption​ (per person)

​$3900

​$3900

The tax owed is ​$12829

.

​(Simplify your answer. Round to the nearest dollar as​ needed.)

You are in the 25 %

tax bracket. The apartment rents for $ 1500

per month. Your monthly mortgage payments would be ​$2200

​,

of which an average of ​$1900

per month goes toward interest during the first year. Determine whether renting or buying is cheaper in terms of monthly payments during the first year. Assume you are itemizing deductions.

Is it cheaper to own or to​ rent?

It is cheaper to rent

.

It is cheaper to own

.