A developer wants to buy a certain parcel of land. The developer believes she can afford payments of $\$ 44,000$ each half-year for the next $7$ years. How much can she borrow and hold to this budget at each of the following interest rates?

(a) $8.9 \%$ compounded semiannually

(b) $7.3 \%$ compounded semiannually

Three weeks ago James worked 46 hours and earned $\$414$. Two weeks ago he earned $\$333$ by working 37 hours. Last week he worked 42 hours for $\$378$. What were his total earnings?

Bill Casler bought a $\$ 2000$, $9$-month certificate of deposit ($\mathrm{CD}$) that would earn $8 \%$ annual simple interest. Three months before the $\mathrm{CD}$ was due to mature, Bill needed his $\mathrm{CD}$ money, so a friend agreed to lend him money and receive the value of the $\mathrm{CD}$ when it matured.

(a) What is the value of the $\mathrm{CD}$ when it matures?

(b) If their agreement allowed the friend to earn a $10 \%$ annual simple interest return on his loan to Bill, how much did Bill receive from his friend?

Two years ago Randi earned $\$18,400$. Last year she earned $\$19,700$. Suppose she earns $\$21,600$ this year. What will be her average earnings per year?

A couple purchasing a home budget $\$ 1800$ per month for their loan payment. If they have $\$ 20,000$ available for a down payment and are considering a $25$-year loan, how much can they spend on the home at each of the following rates?

(a) $6.9 \%$ compounded monthly

(b) $7.5 \%$ compounded monthly

The problem is complex financial problems that require skills from several sections.

Suppose a salesperson invests his $\$ 12,500$ bonus in a fund that earns $10.8 \%$ compounded monthly. Also suppose that he makes contributions of $\$ 150$ at the end of each month to this fund.

(a) Find the future value after $12 \frac{1}{2}$ years.

(b) If after the $12 \frac{1}{2}$ years the fund is used to set up an annuity, how much will it pay at the end of each month for the next $10$ years?

A couple borrowed $\$ 184,000$ to buy a condominium. Their loan was for $25$ years, and money is worth $6 \%$ compounded monthly.

(a) Find the size of their monthly payment.

(b) Find the total amount they would pay over $25$ years.

( c ) Find the total interest they would pay over $25$ years.

(d) Find the unpaid balance after $7$ years.

A woman makes $\$ 3000$ contributions at the end of each half-year to a retirement account for a period of $8$ years. For the next $20$ years, she makes no additional contributions and no withdrawals.

(a) If the account earns $7.5\%$ compounded semiannually, find the value of the account after the $28$ years.

(b) If this account is used to set up an annuity that pays her an amount at the beginning of each $6$-month period for the next $20$ years, how much will each payment be?

Seana wants to save $\$ 20,000$ toward the purchase of a new car. She can contribute $\$ 400$ at the beginning of each month into an account that earns $4.8 \%$ compounded monthly. How long until she reaches her goal?

Explain what happens to total revenue in the following scenarios. a. Price decreases and demand is elastic. b. Price decreases and demand is inelastic. c. Price increases and demand is elastic. d. Price increases and demand is inelastic. e. Price increases and demand is unitary elastic. f. Price decreases and demand is perfectly inelastic. g. Price increases and demand is perfectly elastic.

How much more interest will be earned if $\$ 5000$ is invested for $6$ years at $7 \%$ compounded continuously, instead of at $7 \%$ compounded quarterly?

If an initial investment of $\$ 2500$ grows to $\$ 38,000$ in $18$ years, what annual interest rate compounded annually did this investment earn?

Explain what happens to total revenue in the following scenarios. a. Price decreases and demand is elastic. b. Price decreases and demand is inelastic. c. Price increases and demand is elastic. d. Price increases and demand is inelastic. e. Price increases and demand is unitary elastic. f. Price decreases and demand is perfectly inelastic. g. Price increases and demand is perfectly elastic.

A woman buys a car for $\$ 40,000$. If the interest rate on the loan is $12 \%$ compounded monthly and she wants to make monthly payments of $\$ 700$ for $3$ years, how much must she have for a down payment?