FINANCE CH5

Paul Springer plans to save for a down payment for a house in 10 years. He will be able to invest $12,000 today in a money market account that will pay him an interest of 5.50 percent on a monthly basis. How much will he have at the end of 10 years?

$20,773

roy Gross is considering an investment that pays 7.00 percent, compounded annually. How much will he have to invest today so that the investment will be worth $29,000 in six years?

19323.92

Your birthday is next week and instead of other presents, your parents promised to give you $2,000 in cash. Since you have a part-time job and, thus, don't need the cash immediately, you decide to invest the money in a bank CD that pays 5.00 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time?

2208.97

Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 10 percent each year. What will be the value of the investment in 10 years?

64843.56

our aunt is planning to invest in a bank CD that will pay 10.00 percent interest semi-annually. If she has $6,000 to invest, how much will she have at the end of four years?

8864.7327

Why is a dollar today worth more than a dollar one year from now?

A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true.

What is a time line, and why is it important in financial analysis?

A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as timing of each cash flow has a big impact on the final figure, and therefore on the resulting investment decision.

What is compounding, and how does it affect the future value of an investment?

Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value at the end of the time period will be assuming the initial investment will earn interest, which is reinvested and will earn additional interest in the future periods.

What is the present value, and when is it used?

Present value is the amount a future sum is worth today given a certain return rate. The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future.

Anne Morgan wants to borrow $6,000 for a period of four years. She has two choices. Her bank is offering to lend her the amount at 7.25 percent compounded annually. She can also borrow from her firm and will have to repay a total of $8,130.93 at the end of four years. Should Anne go with the bank or the firm, and what is the interest rate if she borrows from her firm?

She should borrow from the bank as the bank is charging a lower interest rate than the firm's interest rate of 7.9%.

What is the difference between simple interest and compound interest?

The difference is the interest earned on interest.

Explain why you would expect the discount factor to become smaller when based on the longer the time to payment.

The discount factor will become smaller the longer the time to payment due to time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 + i)n. The longer the time to payment, the larger n gets, which will make the discount factor smaller.

What is the discount rate? How does the discount rate differ from the interest rate in the future value equation?

The discount rate is the compound interest rate used to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used.

What is the difference between the interest rate (i) and the growth rate (g) in the future value equation?

The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as sales or change over time. When referring to money being invested, we use the term interest rate.

How does changing the compounding period affect the amount of interest earned on an investment?

The more frequent the compounding schedule, the higher the interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn you $10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10.38.

What is the relation between the present value factor and the future value factor?

The present value factor is the reverse of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 + i).

The present value of future cash flows:

increases as the discount rate decreases.

time value of money

is the difference between a dollar in hand today and a dollar promised in the future

Compounding

is the process of increasing cash flows to a future value

Discounting

is the process of reducing future cash flows to a present value

Present Value

measures the current value of future cash flows discounted at the appropriate interest rate

Future Value

measures the value of an investment after it earns interest for one or more periods

Money has time value because

people can earn interest on money that is invested

Total compound interest is the

sum of simple interest and the interest on interest