Chapter Questions
If Samantha invests $$\$ 700$$ today in an account that pays 4 percent interest compounded annually, how much will she have in her account four years from today?
Fifteen (15) years ago, your parents purchased an investment for $$\$ 2,500$$. If the investment earned 6 percent interest each year, how much is it worth today?
Fiona plans to invest $$\$ 500$$ later today. She wants to know to what amount her investment will grow in 20 years if she earns 12 percent interest compounded (a) annually, (b) quarterly, and (c) monthly.
Staci invested $$\$ 950$$ five years ago. Her investment paid 7.2 percent interest compounded monthly. Staci's twin sister Shelli invested $$\$ 900$$ at the same time. But Shelli's investment earned 8 percent interest compounded quarterly. How much is each investment worth today?
What is the present value of $$\$ 1,500$$ due in 14 years at a (a) 5 percent interest rate and (b) 10 percent rate. Explain why the present value is lower when the interest rate is higher.
Matt is considering the purchase of an investment that will pay him $$\$ 12,500$$ in 12 years. If Matt wants to earn a return equal to 7 percent per year (annual compounding), what is the maximum amount he should be willing to pay for the investment today?
What is the present value (PV) of an investment that will pay $$\$ 2,500$$ in five years if the opportunity cost rate is 9 percent compounded (a) annually, (b) quarterly, and (c) monthly? Explain why the $\mathrm{PV}$ is lowest when interest is compounded monthly.
If Quincy can invest at an opportunity cost rate equal to 12 percent compounded monthly, what lump-sum amount should he invest today so that he has $$\$ 22,000$$ to buy a new car in three years?
Suppose you invest $$\$ 385$$ at the end of each of the next eight years. (a) If your opportunity cost rate is 7 percent compounded annually, how much will your investment be worth after the last $$\$ 385$$ payment is made? (b) What will be the ending amount if the payments are made at the beginning of each year?
At the end of each of the past 14 years, Vanessa deposited $$\$ 450$$ in an account that earned 8 percent compounded annually. (a) How much is in the account today? (b) How much would be in the account if the deposits were made at the beginning each year rather than at the end of each year?
Kym plans to deposit $$\$ 100$$ in an account at the end of each month for the next five years so that she can take a trip. (a) If Kym's opportunity cost rate is 6 percent compounded monthly, how much will she have in the account in five years? (b) How much will be in the account if the deposits are made at the beginning of each month?
Suppose your opportunity cost rate is 11 percent compounded annually. (a) How much must you deposit in an account today if you want to pay yourself $$\$ 230$$ at the end of each of the next 15 years? (b) How much must you deposit if you want to pay yourself $$\$ 230$$ at the beginning of each of the next 15 years?
Compute the amount Amanda must deposit in an account today so that she can pay herself $$\$ 450$$ per month for the next nine years if her opportunity cost rate is 8.4 percent compounded monthly. How much must Amanda deposit today if she wants to pay herself at the beginning of each month?
Rebecca would like to set up an account to supplement her parents' retirement income for the next 15 years. (a) If the account earns 7.2 percent compounded monthly, how much will Rebecca have to deposit today so that her parents are paid $$\$ 150$$ at the end of each month? (b) How much would she have to deposit if her parents wanted to receive the $$\$ 150$$ payment at the beginning of each month?
If the opportunity cost rate is 7.5 percent, what is the present value of an investment that pays $$\$ 500$$ at the end of this year, $$\$ 400$$ at the end of the next year, and $$\$ 300$$ at the end of the following year? What is the present value if the payments are made at the beginning of each year?
Suppose Jennifer deposits $$\$ 500$$ in an account at the end of this year, $$\$ 400$$ at the end of the next year, and $$\$ 300$$ at the end of the following year. If her opportunity cost rate is 7.5 percent, how much will be in the account immediately after the third deposit is made? How much will be in the account at the end of three years if the deposits are made at the beginning of each year?
Compute the present value (PV) of an annuity that pays $$\$ 320$$ forever if the opportunity cost rate is (a) 4 percent, (b) 8 percent, and (c) 10 percent. Why does the PV decrease as the opportunity cost increases?
Ten years ago, Bruce invested $$\$ 1,250$$. Today, the investment is worth $$\$ 3,550$$. If interest is compounded annually, what annual rate of return did Bruce earn on his investment?
Tina owes $$\$ 12,000$$ on her automobile loan, which has an interest rate equal to 4.8 percent compounded monthly. If Tina pays $$\$ 526$$ at the end of each month, how long will it take her to repay the loan?
Mario wants to take a trip that costs $$\$ 4,750$$, but currently he only has $$\$ 2,260$$ saved. If Mario invests this money at 7 percent compounded annually, how long will it take for his investment to grow to $$\$ 4,750$$ ?
CanAm Financial offers investments that pay 12 percent interest compounded monthly, whereas UniMex Financial offers investments that pay 12.25 percent interest compounded semiannually. Which investment offers the better effective annual return?
Yolanda's bank advertises a savings investment that pays 6 percent compounded monthly. What is the investment's (a) annual percentage rate (APR) and (b) effective annual rate $\left(\mathrm{r}_{\mathrm{EAR}}\right)$ ?
William recently graduated from NFA University. While at NFA, William took out a $$\$ 50,000$$ student loan. His loan requires him to make monthly payments for a 10-year period. (a) If the simple annual interest is 4.2 percent, what are William's monthly payments? (b) To the nearest dollar, how much will William owe on his student loan after he makes payments for three years?
When Sarah Jean purchased her house 12 years ago, she took out a 30-year mortgage for $$\$ 220,000$$. The mortgage has a fixed interest rate of 6 percent compounded monthly. (a) Compute Sarah Jean's monthly mortgage payments. (b) If Sarah Jean wants to pay off her mortgage today, for how much should she write a check? She made her most recent mortgage payment earlier today.
Nona purchased a new car earlier today for $$\$ 32,000$$. She financed the entire amount using a five-year loan with a 3 percent interest rate (compounded monthly). (a) Compute the monthly payments for the loan. (b) How much will Nona owe on the loan after she makes payments for two years (i.e., after 24 payments)?