91Ó°ÊÓ

Pierre deposits \(\$ 9,000\) in a certificate of deposit that pays 8\(\%\) interest, compounded semiannually. How much interest does the account earn in the first six months? What is the balance after six months?

John, Paul, and George are having a disagreement over interest rates. John says that 6\(\frac{3}{4} \%\) can be expressed as 6.75\(\%\) . George thinks that 6\(\frac{3}{4}\) can be expressed as \(0.0675 .\) paul remembers converting percents to equivalent decimals and thinks it can be expressed as 0.0675\(\% .\) Who is correct, and who is incorrect? Explain.

Jill has not been able to maintain the \(\$ 1,000\) minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of \(\$ 0.20\) per check and a \(\$ 12.50\) monthly maintenance fill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. $$\begin{array}{|c|c|}\hline & {\text { Number of }} {\text { Checks on }}\\\ \text { Month } & {\text { Statement }} \\ \hline\text { May } & {14} \\\ \hline \text { June } & {19} \\ \hline {\text { July }} & {23} \\\ \hline{\text { August }} & {24} \\ \hline\end{array}$$ a. What is the mean number of checks Jill wrote per month during the last four months? b. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. c. Estimate the total monthly fees Jill will pay each month for the new checking account.

Grandpa Joe wants to open an account for his grandchildren that he hopes will have \(\$ 80,000\) in it after 20 years. How much must he deposit now into an account that yields 2.75\(\%\) interest, compounded monthly, so he can be assured of reaching his goal?

Whitney deposits \(\$9,000\) for two years. She compares two different banks. State Bank will pay her 4.1% interest, compounded monthly. Kings Savings will pay her 4.01% interest, compounded continuously. a. How much interest does State Bank pay? b. How much interest does Kings Savings pay? c. Which bank pays higher interest? How much higher? d. What other factors might affect Whitney’s choice besides interest?

Gary and Ann have a joint checking account. Their balance at the beginning of October was 9,145.87 dollar . During the month they made deposits totaling 2,783.7 dollar, wrote checks totaling 4,871.90 dollar , paid a maintenance fee of 12 dollar, and earned 11.15 dollar in interest on the account. What was the balance at the end of the month?

Kevin has \(x\) dollars in an account that pays 2.2\(\%\) interest, compounded quarterly. Express his balance after one quarter algebraically.

Beth and Mark would like to put some savings in the bank. They most likely will not need this money for 4 years, so Beth wants to put it in a four-year CD. Mark wants to put the money in a passbook savings account. What is the advantage of a CD? What is the disadvantage?

Robbie opens an account at a local bank by depositing \(\$ 100\) . The account pays 2.4\(\%\) interest, compounded weekly. He deposits \(\$ 100\) every week for three years. a. How much is in the account after three years? b. Write the future value function if x represents the number of weeks. c. Use a graphing calculator to graph the future value function. d. Using the graph, what is the approximate balance after 2 years?

Regina deposits \(\$ 3,500\) in a savings account that pays 7\(\frac{1}{2} \%\) interest, compounded semiannually. a. How much interest does the account earn in the first six months? b. What is the balance at the end of the first six months? c. How much interest does the account earn in the second six months? d. What is the balance at the end of the year? e. How much interest does the account earn the first year? f. How much interest would \(\$ 3,500\) earn in one year at 7\(\frac{1}{2} \%\) interest, compounded annually? g. How much more interest does Regina earn at an interest rate of 7\(\frac{1}{2} \%\) compounded semiannually than compounded annually?