Time Value Tools: Program Overview

Transcription

1 Time Value Tools: Program Overview The Time Value Tools program is used to solve three types of Time Value of Money problems: Single Payment, Series of Payments, and Loan Payments. Each problem may be solved for one of the following: present value, future value, payment (annuity), interest rate, time horizon, initial balance, payment level, and time to maturity. There are three sections of this program. The user may choose to evaluate a single payment, series of payments, or loan payments. Problem Type: Single Payment: What is the future value of $1 deposited today? What is the present value of $1 received in the future? Series of Payments: What is the future value of $1 deposited annually for N years? What is the present value of $1 received annually for N years? Loan Payments: What are the monthly payments if I borrow $100 today at an interest rate i for N years? For the problems described above, the user may solve for one of the following variables: Variable Present Value Sample Problem If I deposit $500 in a savings account each month earning 4% interest (compounded monthly) for 1 ½ years, how much is it worth today? Future Value How much will I have if I save $500 every month in an account earning 4% (compounded every 4 weeks) for 1 ½ years? Payment (annuity) What periodic payment will I have to make to receive $10,000 in 1 ½ years with a 4% interest rate compounded every 4 weeks? What amount do I owe every 4-weeks for one year, if I m charged 6% interest for a $100 loan? (not applicable for Single Payment problem) Interest Rate What annual interest rate will compound a series of payments every 4 weeks for 1 ½ years to a future value of $10,000? Time Horizon How long will it take me to accumulate $10,000 if I sav e $200 each month in an account earning 2.5% compounded monthly? Initial Balance What is the original balance of the loan if I m asked to pay $7.94 every 4-weeks for one year with an interest rate of 6%? Payment Level What are the monthly payments I owe, if I borrow $100 for one year charged an interest rate of 6%? Time to Maturity How long do I have to make $7.94 payments every 4-weeks, if I m charged 6% interest for a $100 loan? Solution: The solution for the unknown variable is found in the most bottom cell and is highlighted green. Interpretation: The program provides a descriptive interpretation for each solution describing how the input data is related to the solution. Display/Hide Formulas: This button displays the formula used for the Time Value of Money calculations. Simply click on the Display Formula button. To make the formula disappear, reclick that button which is now called Hide Formula. Sensitivity Charts: For each Single Payment problem, sensitivity charts are made available. The charts graph the relationship between common variables in the problem.

2 Single Payment Example If I deposit a single payment of $100 today, how much will I have in 5 years with an annual interest rate of 4% compounded monthly? This is an example of a Single Payment problem in which the Future Value is unknown. In the blue box below, single payment and future value have been selected. The Inputs are entered in the yellow section below the blue box. The inputs needed for this type of problem include: nominal annual rate: interest rate compounding frequency: the frequency that interest is compounded time horizon in years: length of time present value: the amount you will start with The interest rate is 4% and is compounded every 4-weeks. The length of the analysis is 5 years and the present value, or amount we deposit initially, is $100. As seen in the bottom box, the Future Value (V n ) is $ There is also an interpretation to the right of the inputs that reads The future value of $ received today and compounded for 5 years at 4% per year is $ Present Value: If I m told that I ll receive $2, in 20 years, what is that amount worth today? Future Value: If I deposit $1,000 today into my savings account (4% interest compounded every 4-weeks) how much will I have in 20 years? Interest Rate: At what interest rate will I have $2,200 in 20 years, if I deposit $1,000 today in a CD? Time Horizon: How long do I have to keep my $1,000 deposit in my savings account (4% interest compounded every 4-weeks) if I want to have $3,000?

3 Sensitivity Charts This chart shows the relationship between the present value and the interest rate such that the future value remains constant at a given time horizon. The line on the chart represents the combination of present values and interest rates that produce the same future value at a given time horizon. In this example, the future value is $122 with a 5 year time horizon. This is accomplished by depositing $100 at a rate of 4%, as well as $40 at a rate of 22.5%. This chart shows the relationship between the present value and the time horizon such that the future value remains constant at a given interest rate. The line on the chart represents the combination of present values and time horizons that produce the same Future Value at the given interest rate. In this example, the future value is $122. This is accomplished by depositing $100 for 5 years, as well as depositing $82 for 10 years.

4 Series of Payments Example If I deposit $100 in a savings account every month, earning 4% interest every 4-weeks, how much will I have in 5 years? This is an example of a Series of Payments problem in which the Present Value, is unknown. In the box below, series of payments and present value have been selected. The inputs are entered in the section below the box. The inputs needed for this type of problem include: Nominal annual rate: interest rate Compounding frequency: the frequency that interest is compounded Periodic payment (annuity): amount paid each period Time horizon in years: length of time The interest rate is 4% and is compounded every 4-weeks. The length of the analysis is 5 years. Finally, the annuity payment, or amount we deposit each day, is $100. As seen in the bottom box, the Future Value (V n ) is $7, There is also an interpretation to the right of the inputs that reads The future value of a $ payment every 4 weeks, received per period over 5 years and compounded at 4% per year is $7, Present Value: If I deposit $500 in a savings account each month earning 4% interest (compounded every 4-weeks) for 1 ½ years..how much is it worth today? Future Value: How much will I have if I save $500 every month in an account earning 4% (compounded every 4-weeks) for 1 ½ years? Payment (annuity): What periodic payment will I have to make to receive $10,000 in 1 ½ years with a 4% interest rate compounded every 4-weeks? What amount do I owe every 4-weeks for one year, if I m charged 6% interest for a $100 loan? Interest Rate: What annual interest rate will compound a series of payments every 4-weeks for 1½ years to a future value of $10,000? Time Horizon: How long will it take me to accumulate $10,000 if I save $200 each month in an account earning 2.5% compounded monthly?

5 Loan Payments Example If I borrow $100,000 at a 6% rate for 15 years, what will the semi-annual payments be? This is an example of a Loan Payments problem in which the Payment Level, or amount we owe each period, is unknown. In the blue box below, loan payments and payment level have been selected. The inputs are entered in the yellow section below the blue box. The inputs needed for this type of problem include: Nominal annual rate: interest rate Payment frequency (per year): how often you make payments Time to maturity (years): the time allowed to pay back the loan without penalties Initial loan amount: the original amount of the loan. The interest rate is 6% and is compounded semiannually. The time to maturity is 15 years. Finally, the initial loan amount is $100,000. As seen in the bottom box, the Payment per period (A) is $5, There is also an interpretation to the right of the inputs that reads A series of $5, payments paid semiannually for 15 years at 6% per year pays off the initial loan of $ Initial Balance: What is the original balance of the loan if I m asked to pay $7.94 every 4-weeks for one year with an interest rate of 6%? Payment Level: What are the monthly payments, if I borrow $100 at an interest rate of 6% for one year? Interest Rate: What interest rate am I being charged, if I m asked to pay $7.94 every 4-weeks for one year on a $100 loan? Time to Maturity: How long do I have to make $7.94 monthly payments, if I m charged 6% interest for a $100 loan?