Often in personal finance we want to know what our $1 investment today will be worth in 20 years. In business however, there is more concern with answering the question, “If I receive $100 in 5 years, what is that worth today?” To answer this question, modify the formula fv = pv*((1+i)^n) and use the reciprocal. Simply stated, the reciprocal of a number is 1 divided by the number; the reciprocal of 10, for example, is 1/10. In the formula above, we divide both sides by ((1+i)^n), which creates a new formula where the fv is multiplied by the reciprocal of the original: fv*(1/((1+i)^n))=pv. Select an interest rate and number of periods—be sure your numbers are different from other students who already answered this question—to calculate the present value of $100 received in the future. What would the value of $100 in the future be today given the interest rate and number of periods you selected?
V = Vp(1+r)^n. APR = 10%.
r = (10%/12) / 100% = 0.00833=Monthly %
rate expressed as a decimal.
n = 1Comp./mo * 60mo = 60 Compounding
periods.
V = Vp(1.00833)^60 = $100
Vp = 100 / (1.00833)^60 = $60.77.
To calculate the present value of $100 received in the future, we can use the formula:
PV = FV * (1 / ((1 + i)^n))
Where:
PV = Present Value
FV = Future Value
i = Interest Rate
n = Number of Periods
1. Select an interest rate and the number of periods. Let's assume an interest rate of 5% and a number of periods of 10 years.
2. Plug in the values into the formula:
PV = $100 * (1 / ((1 + 0.05)^10))
3. Simplify the equation:
PV = $100 / (1.05^10)
4. Use a calculator or spreadsheet to calculate the present value:
PV ≈ $61.39
Therefore, the value of $100 received in the future, given an interest rate of 5% and 10-year period, would be approximately $61.39 today.