(a) decide whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Is it more economical to buy an automobile for $\$ 29,000$ cash or to pay $\$ 8000$ down and $\$ 3000$ at the end of each quarter for $2$ years, if money is worth $8 \%$ compounded quarterly?

Annuity Find the future value of an ordinary annuity of $\$ 800$ paid at the end of every $6$-month period for $10$ years, if it earns interest at $12 \%$ compounded semiannually.

Rank each interest rate and compounding scheme in order from highest yield to lowest yield.

$8 \%$ compounded quarterly, $8 \%$ compounded monthly, $8 \%$ compounded annually

A company that purchases a piece of equipment by borrowing $\$ 250,000$ for $10$ years at $6 \%$ compounded monthly has monthly payments of $\$ 2775.51$.

(a) Find the unpaid balance on this loan after $1$ year.

(b) During that first year, how much interest does the company pay?

Suppose you lent $\$ 5000$ to friend $1$ for $18$ months at an annual simple interest rate of $9 \%$. After $1$ year, you need money for an emergency and decide to sell the note to friend $2$.

(a) How much does friend $1$ owe when the loan is due?

(b) If your agreement with friend $2$ means that she earns simple interest at an annual rate of $12 \%$, how much did friend $2$ pay you for the note?

What is the annual percentage yield (or effective annual rate) for a nominal rate of (a) $8.4 \%$ compounded quarterly and (b) $10\%$ compounded continuously?

Chess legend If in the previous problem the king granted the inventor's wish for half a chessboard, how many grains would the inventor receive?

A couple who borrow $\$ 90,000$ for $30$ years at $7.2 \%$ compounded monthly must make monthly payments of $\$ 610.91$.

(a) Find their unpaid balance after $1$ year.

(b) During that first year, how much interest do they pay?

(a) decide whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

A local library receives a bequest of $\$ 100,000$ from a prominent local family. How much will this provide at the beginning of each $3$-month period for the next $2 \frac{1}{2}$ years if money is worth $7.4 \%$ compounded quarterly?

(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Jake Werkheiser decides to invest $\$ 2000$ in an IRA at the end of each year for the next $10$ years. If he makes these investments and if the certificates pay $12 \%$ compounded annually, how much will he have at the end of the $10$ years?

Chess legend Legend has it that when the king of Persia wanted to reward the inventor of chess with whatever he desired, the inventor asked for one grain of wheat on the first square of the chessboard, with the number of grains doubled on each square thereafter for the remaining $63$ squares. Find the number of grains on the $64$th square. (The sum of all the grains of wheat on all the squares would cover Alaska more than $3$ inches deep with wheat!)

(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Parents agree to invest $\$ 500$ (at $10 \%$ compounded semiannually) for their son on the December $31$ or June $30$ following each semester that he makes the dean's list during his $4$ years in college. If he makes the dean's list in each of the $8$ semesters, how much money will his parents have to give him when he graduates?

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

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?