The future value (FV), present value (PV), interest rate (r) and period of investment (t) are related by the formula FV = PV(1 + rt). Let us use this formula and a little algebra to solve for each of the four quantities in terms of the others: FV = PV(1 + rt). PV = FV/(1+rt) r = (FV-PV)/(PV*t) t = (FV-PV)/(PV*r) Formula for FV Formula for PV Formula for r Formula for t
This allows us to set up a little "calculator" that gives any one of these quantities by knowing the other: To set it up, let us use the data from Example 1 in the text: FV = ? PV = 2000 r = 4.75% t=6 Unknown Given Given Given
1. Set it up to compute the future value (FV) by using the formula for FV here. (You did it right if you get a value of $2,570.00 ). Entered Calculated 4.75% 6 $2,000.00
Rate Years Present Value Future Value
r t PV FV
Given values go here. Note: Format the PV and FV cells as currency, and the r cells as percentage. 2. Now fill in the remaining three formulas in the "Calculated" column. 3. Let us now use the calculator to do Example 4 from the text: A US Treasury bill paying $10,000 after 1 year yields 4.50% simple annual interest. How much will you pay for the T-bill? Solution We are given FV = $10,000, t = 1 and r = 4.50%. Enter these values in the "Entered" Column and read off the present value from the "Calculated" column. That is the answer! 4. Treasury Bills Look at Example 5 from the text: A US Treasury bill paying $10,000 after 6 months sells at a discount rate of 4.38%. What does it cost and what simple annual interest rate does it pay? Solution The cost, or present value, of a Treasuty Bill equals the future value (here $10,000) minus the discount. The discount is half (six months' worth) of 0.0438 * 10,000, which you enter here. FV Discnt. Rate $10,000 4.38% Time 0.5 PV $9,781.00
To answer the question, use the above values for FV and PV in our simple interest calculator to obtain the simple interest rate. (It should come out to 4.48% if you do it correctly.)
alculated" column.
nus the discount.
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