# Week 5 Math

INTEREST

8.Elisa needs money to repair her home air conditioner, so she pawns her bicycle. The pawnbroker loans Elisa $270. Ten days later, Elisa gets her bicycle back by paying the pawnbroker $280.50. What annual simple interest rate did the pawnbroker charge Elisa? Assume 360 days in a year. The pawnbroker charged Elisa a simple interest rate of what %?

9.A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity. (The Effective Date is the date the note was written.) Assume the year is not a leap year.

Principal: 4,000 Rate:5% Effective date:May 1rst Partial payment: 2,000 on June 1rst Maturity date:July 1rst

The balance due on the note at the date of maturity is How many dollars?

10.Determine the effective annual yield for $1 invested for 1 year at 7.3% compounded quarterly.

The effective annual yield is what %?

11.Bank A advertises a money market account that pays 1.9%

compounded quarterly. Bank B advertises a money market account that pays 1.8%

compounded daily.

**a)** Determine the annual percentage yield for bank A’s money market account.

**b)** Determine the annual percentage yield for bank B’s money market account.

**c)** Assuming all other factors are equal, which bank’s money market account would be the better investment?

12.Suppose you saw a sign at your local bank that said, ”6.3%

rate compounded quarterly

–

6.6%

Annual Percentage Yield (APY).” Is there anything wrong with the sign? Explain.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

**A.**

Yes. The APY is incorrect. The correct APY is what %?

(Round to the nearest hundredth as needed.)

**B.**

Yes. The number of compounding periods is incorrect. Interest should be compounded daily.

**C.**

No. The information on the sign is correct.

12.A village recently completed the construction of a new water tower. The entire cost of the water tower was $948,000,

and the government paid $370,000

of the total cost through the awarding of a grant. In addition, the village can delay paying the balance of the cost for 30

years (without paying any interest during the 30

years). To finance the balance, the village board will at this time assess its 674

homeowners a one-time flat fee surcharge and then invest this money in a 30-year

CD paying 6.2%

interest compounded monthly.

**a)** What is the balance due on the water tower?

13.A simple formula can help you estimate the number of years required to double your money. It’s called the rule of 72. You simply divide 72 by the interest rate (without the percent sign). For example, with an interest rate of 4%, your money would double in approximately 72÷4,

or 18 years.

**a)** How many years would it take $1000

to double at an interest rate of 2%?

Installment Loans

1.Determine the monthly payment for the installment loan.

Amount Financed:700$, Annual Percentage Rate:7.5%, Number of Payments per Year:12, Time in Years: 1

The monthly payment is how much $?

2.Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4600

to purchase tools and equipment. Landon decides to finance the purchase with a 36-month

fixed installment loan with an APR of 4.5%.

**a)** Determine Landon’s finance charge.

**b)** Determine Landon’s monthly payment.

3.Travis Thompson uses his credit card to obtain a cash advance of $600 to pay for his textbooks in medical school. The interest rate charged for the loan is 0.04203%

per day. Travis repays the money plus the interest after 30

days.

**a)** Determine the interest charged for the cash advance.

**b)** When he repaid the loan, how much did he pay the credit card company?

4.Jamie needs a new roof on her house. The cash cost is $6000.

She decides to finance the project by paying 15.0%

down, with the balance paid in 24

monthly payments of $234.

**a)** What finance charge will Jamie pay?

**b)** What is the APR to the nearest half percent?

5.Ray Flagg took out a 60-month fixed installment loan of $12,000 to open a new pet store. He paid no money down and began making monthly payments of

$221.

Ray’s business does better than expected and instead of making his 30th payment, Ray wishes to repay his loan in full. **a)** Determine the APR of the installment loan.

APR=what percent?

6.Shiing Shen Chern’s credit card company determines his minimum monthly payment by adding all new interest to 1% of the outstanding principal. The credit card company charges an interest rate of 0.043028% per day. On March 17, Shiing uses his credit card to purchase airline tickets for his family for $3900. He makes no other purchases during March. Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer part a.

**a)** Assuming Shiing had no new interest, determine Shiing’s minimum payment due on April 1, his billing date.Shiing’s minimum payment due on April 1 is what amount?

7.On the April 3

billing date, Michaelle Chappell had a balance due of $950.02

on her credit card. From April 3

through May 2,

Michaelle charged an additional $266.69

and made a payment of $600.

**a)** Find the finance charge on May 3,

using the previous balance method. Assume that the interest rate is 1.8%

per month.

**b)** Find the new balance on May 3.

8.The balance on Ramon Felipe’s credit card on January 11,

his billing date, was $238.49.

For the period ending February 11,

Ramon had the following transactions to the right.

a) Find the average daily balance for the billing period.

b) Find the finance charge to be paid on February 11.

Assume an interest rate of 1.2% per month.

c) Find the balance due on February 11

January 20

Charge:

Restaurant meal

$40.51

January 27

Payment

$100.00

February 5

Charge:

Lawn ornaments

$36.89

February 6

Charge: Microwave oven

$196.84

9.On September 6,

the billing date, Verna had a balance due of $566.95

on her credit card. Assume that the interest rate is 1.1% per month. Suppose that Verna’s bank uses the average daily balance method. Sept. 8

Payment

$280.00

Sept. 23

Charge: Airline ticket

$329.00

Sept. 25

Charge: Hotel bill

$191.52

Oct. 2

Charge: Clothing

$84.64

Determine Verna’s average daily balance for the billing period from September 6

to October 6.

The average daily balance for the billing period was how much?

Mortgages

1.Determine the monthly principal and interest payment for a 15-year mortgage when the amount financed is $65,000 and the annual percentage rate (APR) is 5.0%.

The monthly principal and interest payment is what amount?

2.Anna is buying a house selling for $295,000.

To obtain the mortgage, Anna is required to make a 20%

down payment. Anna obtains a 25-year

mortgage with an interest rate of 4%.

**a)** Determine the amount of the required down payment.

**b)** Determine the amount of the mortgage.

**c)** Determine the monthly payment for principal and interest.

3.The Nicols are buying a house selling for $435,000.

They pay a down payment of $35,000

from the sale of their current house. To obtain a 20-year

mortgage at a 6.5%

interest rate, the Nicols must pay 1.5

points at the time of closing.

**a)** What is the amount of the mortgage?

**b)** What is the cost of the 1.5

points?

4.The Adeeva’s gross monthly income is $6900.

They have 18 remaining payments of $210

on a new car. They are applying for a 30-year,

$223,000

mortgage at 7.5%.

The taxes and insurance on the house are $400

per month. The bank will only approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners’ insurance that is less than or equal to 28% of their adjusted monthly income.

**a)** Determine 28% of the Adeeva’s adjusted monthly income.(Round to the nearest cent.)

5.Laura and Martin obtain a 30-year,

$160,000

conventional mortgage at 8.5%

on a house selling for $200,000.

Their monthly mortgage payment, including principal and interest, is $1230.40.

a) Determine the total amount they will pay for their house.

b) How much of the cost will be interest?

c) How much of the first payment on the mortgage is applied to the principal?

6.The Bells obtain a 25-year,

$110,000

conventional mortgage at a 9.0%

rate on a house selling for $150,000.

Their monthly mortgage payment, including principal and interest, is $924.00.

They also pay 3

points at closing.

**a)** Determine the total amount the Bells will pay for their house.

**b)** How much of the cost will be interest (including the 3

points)?

**c)** How much of the first payment on the mortgage is applied to the principal?

7.Kathy wants to buy a condominium selling for $95,000. The taxes on the property are $1400 per year, and homeowners’ insurance is $326 per year. Kathy’s gross monthly income is $4500. She has 15 monthly payments of $145 remaining on her van. The bank is requiring 20% down and is charging a 9.5% interest rate with no points. Her bank will approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners’ insurance that is less than or equal to 28% of her adjusted monthly income.

**a)** Determine the required down payment.

8.The Ruffins are negotiating with two banks for a mortgage to buy a house selling for $185,000. The terms at bank A are a 15% down payment, an interest rate of 10%, a 25-year conventional mortgage, and 2 points to be paid at the time of closing. The terms at bank B are a 10% down payment, an interest rate of 11.0%, a 30-year conventional mortgage, and no points. Which loan should the Ruffins select in order for the total cost of the house to be less?

9.The Bhatts purchased a new home for $238,000

with a down payment of $46,000.

They obtained a 20-year

adjustable rate mortgage with the following terms. The interest rate is based on the one-year Treasury bill rate, which is currently at 0.5%,

and the add-on rate, which is 3.5%.

The initial rate period is 5 years, and thereafter the interest rate is adjusted once a year and a new monthly mortgage payment is calculated.

**a)** Determine the Bhatts’ initial ARM rate.

**b)** Determine the Bhatts’ initial monthly payment for principal and interest.

**c)** If, after the 5-year initial rate period, the rate of the one-year Treasury bill rises to 2.0%,

determine the Bhatts’ new ARM rate.