(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?

Use the compound interest table on the page in lesson mentioned to find the annual interest earned. Then calculate the effective rate of interest.

Rebecca Ellis' bank pays $8 \%$ annual interest on savings accounts, compounded quarterly. On April $1$, she made a deposit of $\$ 1,500$ to her savings account, which had a balance of $\$ 400$. a. She makes no other deposits or withdrawals to the account for one year. On the following April $1$ what will her account balance be? b. What interest amount will she have earned? c. The interest named in part b represents what effective rate of interest, to the nearest hundredth percent?

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?

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

An insurance settlement of $\$ 1.5$ million must replace Trixie Eden's income for the next $40$ years. What income will this settlement provide at the end of each month if it is invested in an annuity that earns $8.4 \%$ compounded monthly?

A savings account deposit of $\$ 8,500$ is made on April $1$ and kept on deposit for $3$ months. The account earns $5.4 \%$ annual interest, compounded quarterly. What amount of interest is earned on the deposit for three months?

Find the interest paid and the balance for each date listed in each savings account. Write your answers in the table. Interest is compounded quarterly on January $1$, April $1$, July $1$, and October $1$. Semiannual interest is paid on January $1$ and July $1$.

Find the interest for one interest period for each exercise. Round your answers to the nearest cent. Write your answers in the amount of interest column.

Find the annual percentage yield for an investment at

(a) $7.3 \%$ compounded monthly

(b) $6 \%$ compounded continuously.

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

Comparing yields Find the annual percentage yield equivalent to a nominal rate of $7.2 \%$ (a) compounded quarterly and (b) compounded continuously.

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

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?

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