# MTH 216 Week 5 Study Plan for Final Examination

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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.

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 \$128 per month on food.

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

51% 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 \$300 co-payment. Surgical operations have a \$1 comma 200 deductible (the first \$1 comma 200 is paid out of pocket). The monthly premium is \$390. 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
\$100100
Mar. 26:Emergency room
\$580580
Apr. 23: Office visit
\$100100
May 14: Surgery
\$6 comma 5006,500
July 1: Office visit
\$100100
Sept. 23: Emergency room
\$950950
a. 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 \$

6555.

(Type a whole number.)

b. 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 \$

8330.

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

You invest \$3000 in an account that pays simple interest of 2% for 20 years.

The amount of money you'll have at the end of 20 years is \$

4200.

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

A bank offers an APR of 4.6% compounded daily.

The annual percentage yield is

4.71%.

(Do not round until the final answer. Then round to two decimal places as needed.)

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 \$19 comma 000 deposit in an account with an APR of 3.5%.

The balance in the account after 1 year is approximately \$

19676.77.

(Round to the nearest cent as needed.)

The balance in the account after 5 years is approximately \$

22633.68.

(Round to the nearest cent as needed.)

The balance in the account after 20 years is approximately \$

38261.30.

(Round to the nearest cent as needed.)

The APY for the account is approximately

3.56%

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 4 %. How much should you deposit monthly to accumulate \$81 comma 000 in 15 years?

You should invest \$

329.15 each month.

Compute the total and annual returns on the described investment.

Four years after buying 200 shares of XYZ stock for \$50 per share, you sell the stock for \$ 15 comma 100.

The total return is

51%.

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

The annual return is

10.9%.

Consider a home mortgage of \$150 comma 000 at a fixed APR of 3% for 15 years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

a. The monthly payment is \$

1035.87.

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

b. The total amount paid over the term of the loan is \$

186456.6.

(Round to the nearest cent as needed.)

c. Of the total amount paid,

80.4% is paid toward the principal, and

19.6% is paid for interest.

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 \$100 000 loan.

Option 1: a 30-year loan at an APR of 9.5%.

Option 2: a 15-year loan at an APR of 9%.

Find the monthly payment for each option.

The monthly payment for option 1 is \$

840.85.

The monthly payment for option 2 is \$

1014.27.

(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 \$

302706.

The total payment for option 2 is \$

182568.6.

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

B.

Option 2 will always be the better option

C.

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

D.

Option 1 will always be the better option.

A man earned wages of \$31 comma 200, received \$1900 in interest from a savings account, and contributed \$3100 to a tax-deferred retirement plan. He was entitled to a personal exemption of \$3200 and had deductions totaling \$5340. Find his gross income, adjusted gross income, and taxable income.

His gross income was \$

His adjusted gross income was \$

His taxable income was \$

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

Sarah is single and had a taxable income of \$35 800.

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 \$

4924.

You are in the 25 % tax bracket. The apartment rents for \$ 1300 per month. Your monthly mortgage payments would be \$1900, of which an average of \$1600 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 own.

It is cheaper to rent.