If you put $1,000 into an account on January 1, 2016 it will earn 5% interest and interest compounds each year.
You will withdraw $300 at the beginning of the year, but invest another $1,000 at the beginning of next year.
The solution to this problem is provided by the data in Table 4A.
You earn $50 in interest during the year.
$50 of interest earned on the $1,000 initial deposit in 2016 becomes part of the beginning balance on which interest is paid.
At the end of the year, the balance in your account is almost $2,000.
We have allowed interest to compound once a year.
Interest on many investments compounds more frequently than that.
Suppose you invest $1,000 on January 1, 2016 in an account that pays 5% interest.
You have a plan to withdraw $300 after one year and to deposit an additional $1,000 after two years.
Let's assume that interest is paid and compounded twice a year.
Table 4A.2 contains the relevant calculations.
There is a correlation between larger returns and more frequent compounding.
The end-of-2018 account balance is 5% compounded annually while the end-of-2018 account balance is 5% compounded semiannually.
When interest compounds just once per year, you are earning a lower rate of interest, but with semiannual compounding, you are earning a higher rate of interest.
The true rate of interest is more than the stated rate.
The true rates of interest are shown in Table 4A.3.
A stated interest rate is 5.127%.
The true rate of interest associated with various alternatives should be evaluated before making a deposit because of the impact that differences in compounding frequencies have on return.
Proper investment analysis requires computations that take into account the time value of money, which can be quite tedious to perform by hand.
You can use financial calculator and spreadsheets to streamline the application of time value of money techniques if you know how to use them.
Preprogrammed financial routines are included in financial calculators.
We show the keystrokes for financial computations throughout the book.
We use 4 of the 5 keys in the left column.
The unknown value is represented by one of the keys.
Some of the more sophisticated calculators have menu-driven keys.
The calculator will prompt you to input each value after you select the appropriate routine.
There is no need for a compute key to get a solu tion on these calculators.
Once all values are input functions, the computed key is used to initiate financial calculation.
The reference guides that accompany the financial calcula tors explain the keystrokes.
You will want to use a calculator once you understand the basics.
You can increase the speed and accuracy of your computations with a little practice.
The objective is conceptual understanding of the material.
Don't just settle for answers because an ability to solve problems with a calculator doesn't necessarily reflect an understanding.
You have to work with the material until you are sure that you also understand the concepts.
Today's investors need the ability to use spreadsheets.
It's never too early to start saving for retirement.
A number is provided in the text.
If you placed $2,000 per year of spreadsheet solutions that identify the cell entries for calculating time value for the next eight years into an of money results.
The value for each variable is entered in a cell in the spread account that earned 10% and left sheet, and the calculation is programmed using an equation that links the indi those funds on deposit in 40 years.
If you change the values of the variables, the solution will grow to more than $500,000.
The equation that determines the calculation is shown at the bottom of the spreadsheet solutions in this book.
The key time value of money is the beginning of the concept.
Consider a deposit of $1,000 that is earning 8% compounded annually.
The future value of this deposit is calculated using the formula below.
The $1,080 balance would earn 8% interest if it stayed on deposit for another year.
At the end of the second year, there would be $1,166.40 in the account.
The beginning-of-year balance is $1,080 and 8% of it is interest.
The value at the end of the second year would be calculated.
The future value can be calculated using a financial calculator.
To calculate the future value, depress CPT and FV.
The number of payments can be set in many calculators.
Most of the calculator are preset for monthly payments.
It's important to make sure your calculator is set for 1 payment per year because we work primarily with annual payments.
It is important to make sure that your calculator is set on the END mode because most are preset to recognize all payments at the end of the period.
You can get instructions for setting these values from the reference guide that accompanies your calculator.
If you want to avoid including previous data in current calculations, you have to clear the register of your calculator.
The known values can be entered in any order.
Inflows are different from outflows with a negative sign.
The -1,000 present value is considered an investment cash outflow or cost if it was scratched as a negative number.
The calculated future value of 1,166.40 is a positive value to show that the payoff is a result of the calculated future value.
The calculator will display the future value of $1,166.40 as a negative number if you key in the $1,000 present value as a positive number.
The present value and future value cash flows will have different signs.
$1,000 per year for eight years is an example of an annuity.
The future value of an annuity is often calculated by investors.
You can find the future value of an annuity by using a calculator or spreadsheet.
Future value is the inverse of present value.
Future value calculations determine how much money will accumulate over time based on some investment you make today.
Present value calculations help investors decide how much they should pay for an investment that promises cash payments later on.
It is the rate of return that the investor requires.
You can buy an investment that will pay $1,000 in a year.
The present value of $1,000 to be received one year from now is $925.93.
If you deposited $925.93 today into an account paying 8% interest, your money will grow to $1,000 in a year.
It is more difficult to find the present value of a sum than it is for a one-year investment.
The technique for finding the present value of a single sum was illustrated in the preceding paragraphs.
We need to calculate the present value of a stream of cash payments because most investments pay out cash at various future dates rather than as a single lump sum.
Individual lump sum pay ments can be viewed as a stream of payments.
Table 4A.4 shows a mixed stream and annuity that make five end-of-year cash payments.
We must calculate the present value of each payment and then add them up to find the present value of these streams.
The table shows the present value calculations for each cash flow in the mixed stream.
The present value of all future cash flows is $193.51 if we find all of the individual present values.
The present value of a mixed stream can be calculated using a financial cal culator or an excel spreadsheet.
The present value of individual cash flows can be found using a financial calculator.
To get the present value of the mixed stream, you sum the individual present values.
Most financial calculators allow you to enter all cash flows, specify the discount rate, and then calculate the net present value of the entire return stream using the NPV func tion on the calculator.
The present value of the mixed stream can be calculated using the following spreadsheet.
The present value of an annuity can be found the same way as the present value of a mixed stream.
The present value of the annuity can be calculated using the following spreadsheet.
Discuss and contrast the terms.
Compare and contrast the concepts of future value and present value.
The present value is calculated using the discount rate.
After reading this appendix, you should know what I IMPortaNt CoNCEPtUaL tooLS is.
Money has a time value on their funds.
Simple interest or compound continuous compounding is how 4A.4 and 4A.5 are applied.
The present value can be calculated when the stream is an annuity.
You can get a personalized study plan if you take the appendix test and log into MyFinanceLab.
The table shows a number of transactions in a savings account.
The owner of the account withdraws the interest as soon as it is paid.
A new table should show the account balance at the end of the year and the interest earned.
A $223 deposit left in an account will pay a 7% annual interest for eight years.
At the end of eight years of a $300 annual deposit into an account, the future value will be.
If interest compounds annually, calculate the future value at the end of the investment period.
If you use a financial calculator or spreadsheet, you can calculate the future value in four years of $15,000 invested in an account that pays a stated annual interest rate of 10%.
You can earn 9% on the investments.
Five years from purchase, a Florida state savings bond can be converted to $1,000.
Compare your answer to the problem before it.
Assume a 12% dis count rate and find the present value of each of the streams of income.
The table shows the streams of income.
To find the present value of each income stream, use a 1% discount rate and then repeat those calculations using an 8% discount rate.
The undiscounted total income in each case is $10,000, so compare the present values and discuss them.
The present value of the annual end-of-year payments is calculated for each of the investments below.
To calculate the following, use a financial calculator or an excel spreadsheet.
The present value of $500 will be received four years from now.
The present value of the income streams is assumed to be at the beginning of the year.
Any of the following investments can be made by Terri Allessandro.
The pur chase price, lump-sum future value, and year of receipt are given for each investment.
There is a 10% rate of return on investments that are similar to those currently under consideration.
Evaluate each investment to see if it's worth the time and money.