You deposit $8,200 into a savings account with an annual percentage rate (APR) of 5.2%.

a. Compute the amount of interest you earn after one year.____________

b. Complete the following table.

Year

Beginning

Interest

End

1

$8,200

2

c. Find an equation which you can use to compute the balance in your account after n years.Use the discrete growth model.____________

d. Use your answer from part c to compute the balance in your account after nine years.____________

The price of a laptop computer is decreasing at the rate of 3% per year.

a. If the component costs $800 today, calculate the price of the computer in one year.____________

b. Find an equation which you can use to compute the price of the computer after n years.Use the discrete model.____________

c. Use your answer from part b to compute the price of the computer after six years. ____________

The price for one share of stock in a company was $44.59 on 2019 June 01.It grew 384.32% between 2019 Jun 01 and 2020 June 01.It grew by 180.84% between 2020 June 01 and 2021 June 2021.

a. Find the price of one share of this company's stock on 2020 June 01.____________

b. Find the price of one share of this company's stock on 2021 June 01.____________

c. Calculate the average annual percent change in one share of this company's stock for the two-year period between 2019 June 01 and 2021 June 01.Use the discrete model or the RATE command.Express your answer as a percent rounded to the nearer tenth.____________

d. Calculate the geometric mean rate of return for the two-year period.Express your answer as a percent rounded to the nearer tenth.____________

The house in which I grew up sold for $172,500 in 2005.Today, in 2021, it has a value of $330,020.

a. Find the annual growth rate of the value of this property.Use the continuous model.Present your answer as a percent rounded to the nearer hundredth.____________

b.Find an equation which you can use to model the price of this house n years after 2005.Use the continuous model.____________

c. Use your answer from part b to forecast the price of this house in 2027.Round your answer to the nearer dollar.____________

Use the following information to answer questions 5 and 6.The NASDAQ stock index closed at 500.84 on 1991 April 15.It had risen to 14,038.76 on 2021 April 15.

a. Calculate the percent change in the NASDAQ index over that period.Round your answer to the nearer thousandth of a percent.____________

b. Calculate the percent change per year in the NASDAQ index over that period.Round your answer to the nearer thousand of a percent.Use the discrete model or the RATE command.____________

c. Use your answer from part b to formulate a model which can estimate the level of the NASDAQ index for any year after 1991.Use the discrete model.Let your independent variable (i.e. n) represent the number of years since 1991.____________

a. The Consumer Price Index was 135.200 in April of 1991; it was 267.054 in April of 2021.Calculate the percent change per year in the Consumer Price Index over that period.Use the RATE command or the discrete model.Round your answer to the nearer thousandth of a percent.____________

b. As measured by the NASDAQ index, has the buying power of funds invested in the stock market increased or decreased over the past 30 years?____________

More Formal Formula

Less Formal Formula

Continuous Model

F = Peⁱⁿ

new = old(e^(rate)(time))

Discrete Model

F = P(1 + i)ⁿ

new = old(1 + rate)^time

The value of certain automobile loses 10% of its value each year.

a. If the automobile sells new for $40,000, calculate its value after one year.____________

b. Find an equation which you can use to compute the price of the computer after n years.Use the continuous model.____________

c. Use your answer from part b to forecast the value of this automobile once it becomes eight years old.____________

The equation F = 13,585e^0.010149x models the population of Fairfax County where x is the number of years since 1960.

a. Find an equivalent equation in the discrete model format.____________

b. Use either model to estimate the population of Fairfax County in 2020.____________

Excel Command

Syntax

Future Value

=FV(rate,nper,pmt,pv)

Number of Periods

=NPER(rate,pmt,pv,fv)

Payment

=PMT(rate,nper,pv,fv)

Present Value

=PV(rate,nper,pmt,fv)

Rate

=RATE(nper,pmt,pv,fv)

When answering the questions 9 through 18, please specify the Excel command you used, including all its parameters, for part a.

Your most recent credit card statement shows an ending balance of $776.04.Your bank offers you the option of paying it with monthly payments of $30 at an annual interest rate of 15.72%.If you take advantage of this offer, how many months will it take you to retire this debt (assuming that you make no future charges to this account)?If your answer is not an integer, use the next higher integer for your answer.(For example, if your answer is 8.1 months, use 9 months for your answer.)

a. Excel command____________

b. answer____________

c. How much interest will you pay over the course of the loan?____________

You are beginning to plan for retirement and have analyzed your personal budget.You start by concluding that you can afford to save $503 per month and believe that your investments can earn an average of 6.6% per year during the period you are saving.If your goal is to have a balance of $869,000 in order to retire, how long will you need to save in order to reach your goal?Present your answer using the next highest integer.(If your answer is 498.1 months, use 499 for your answer.)

a. Excel command____________

b. answer____________

Suppose you make monthly deposits of $279 into your retirement plan.Calculate your balance after 37 years if your account averages an annual rate of return of 5.5%.

a. Excel command____________

b. answer____________

c. How much money will you have deposited into this account over the 30 years?____________

d. How much interest will you have earned in this account over the 30 years?____________

How much must you deposit today, in an account which earns 3.5% annually, if you want to have $86,000 nine years from now?

a. Excel command____________

b. answer____________

Suppose you settle on a retirement goal of $767,400 which you would like to have 47 years from now.How much do you need to invest per month in an account which grows at an annual rate 6.8% in order to meet your goal?

a. Excel command____________

b. answer____________

c. How much money will you have deposited into this account over the 47 years?____________

d. How much interest will you have earned in this account over the 47 years?____________

Suppose you deposit $8,700 in an account which pays interest compounded quarterly.What interest rate would need to earn for your balance to reach $9,715 in one-and-one-half years?

a. Excel command____________

b. answer____________

Suppose you have decided to purchase an automobile.You analyze your personal budget and decide you can afford monthly payments of $282 for seven years.If your loan carries an annual interest rate of 8.48%, what the highest priced car you can afford?

a. Excel command____________

b. answer____________

Suppose you purchase a home for $565,000.You make a down payment of 3% of the purchase price and finance the remainder with a mortgage loan at an annual interest rate of 4.23% for a term of 30 years.

a. How much is the down payment?____________

b. How much did you borrow?____________

c. Calculate the monthly payment on the loan.Round your answer to the nearer cent.

1. Excel command____________

2. answer____________

d. Assuming you don't pay off your loan early, how much interest will you pay on the loan?____________

You are interested in depositing $380 per month into an account which you hope will grow to $660,000 in 39 years.What interest rate will allow your account to reach your goal?

a. Excel command____________

b. answer____________

Suppose you invest $14,500 in a certificate of deposit with an annual percentage rate of 2.8%.How much is your investment worth after eight years?

a. Excel command____________

b. answer____________

Find the geometric mean of 13, 83, 19, 49, and 74.Round your answer to the nearer thousandth.____________

At the end of the most recent month and before interest charges, your credit card account had a balance of $752.46 and an average daily balance of $533.73.Your bank charges 1.62% interest per month.

a. Calculate the amount of interest the bank will charge your credit card account using the average daily balance method.Round your answer to the nearer cent.____________

b. Calculate the balance on your account after the bank adds its interest charges.____________

Day Purchase Payment Balance 5953.82 1 5953.82 2 557.91 $1,021.78 3 51,02 1. 78 4 $51.20 $960. 58 5 $960. 58 E 5960. 58 7 558.20 51,019. 28 8 $1,019. 28 9 525 .75 $1,045.04 1'] $1,045.04 11 $1,045.04 12 $1,045.04 13 $1,045.04 14 $98.92 $945.12 15 522.88 51,0191!) 15 51,0191!) 1? 550.22 51,079. 22 18 $202.89 5875. 33 19 5875. 33 2D 5875. 33 21 5875. 33 22 5875. 33 23 585 .38 5961. 7 1 24 $2 .94 5969. 55 25 5969. 55 26 5969. 55 27 $88.55 583 LCD 28 552.59 5938.59 29 5938. 59 30 $938.59 ending balance $971.35 average daily balance $12.15 interest $950.74 new balance