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Worksheet #23 - Present and Future Value
Spring 2007
Objectives
- How to compute the value of today’s money in the future
- How to compute future money in today’s dollars
- Applications include pricing a bond, a service contract, or a stock in-vestment
Present and Future Value
- Assumption is that money and investment grow exponentially.
- The growth rate of a long-term (30 year) Treasury bond is used as abenchmark since these bonds are low-risk.
- Formulas for Future Value (when given annual or continuous rates) F = P (1 + r)t^ F = P · ert
- Formulas for Present Value (when given annual or continuous rates) P = F/(1 + r)t^ P = F · e−rt
Fill in the charts with either the future or present values assuming a 5%annual interest rate. r = 5% 1 year 2 years 3 years 4 years $ $
multiply the previous year by (1 +Use the^ F^ =^ P^ (1 +^ r)t^ formula to advance $200 to the proper year or just r) to make the money grow one year at a time. Use P = F (1 + r)−t^ to backtrack the $4000 dollars. r = 5% 1 year 2 years 3 years 4 years $200 200(1.05)^4 4000(1.05)^4 $
Find out the present value of these payments. This is a type of bond payment.How much would you pay for this bond? Assume this is an annual rate. r = 10% 1 year 2 years 3 years 4 years 100 100 100 1000 + 100
Backtrack all the future payments into present value dollars. The sum of thepresent values is equivalent to the value of the future payments. It is the most you should be willing to pay if you could invest your money and earn10% each year. After seeing the answer, does it make sense why this should be the answer? r = 10% 1 year 2 years 3 years 4 years 90.90 100 82.64 100 75.13 100 751.31 1000 + 100 Make Sense = 1000.00 100 100 100 1000 + 100
What would be the loan payment that you would receive if you lend $2000at a fair interest rate (8% annual rate) for four years? For each payment, compute the present value of L dollars. These numbers should sum to $2000. r = 8% 1 year 2 years 3 years 4 years L L L L 2000
into the problem, you have to use variables and use formulas that would tellBacktrack each of the payment amounts^ L. Since you don’t know^ L^ going you the present value of each of the future payments. With all the presentvalues of the payments, sum the present values and set them equal to the loan amount. You can now factor out the L and divide to get the value of L. 1.^ L 08 +^1 .L 082 +^1 .L 083 +^1 .L 084 = 2000 L^ {^1.^108 + (^1). 0812 + (^1).^1083 + (^1). 0814 } = 2000 L { 3. 3121 } = 2000 L = (^32000). 3121 = 603. 84 So, payments of $603.84 over four years is equivalent to $2000 today.
