Present value of a future sum
The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations.
The present value (PV) formula has four variables, each of which can be solved for:
1. PV is the value at time=0
2. FV is the value at time=n
3. i is the rate at which the amount will be compounded each period
4. n is the number of periods (not necessarily an integer)
Present value of an annuity for n payment periods
In this case the cash flow values remain the same throughout the n periods. The present value of an annuity (PVA) formula has four variables, each of which can be solved for:
1. PV(A) is the value of the annuity at time=0
2. A is the value of the individual payments in each compounding period
3. i equals the interest rate that would be compounded for each period of time
4. n is the number of payment periods.
To get the PV of an annuity due, multiply the above equation by (1 + i).
Present value of a perpetuity
When tends to infinity, the PV of a perpetuity (a perpetual annuity) formula becomes simple division.
When this is an increasing perpetuity, this i becomes i’ 1+i’=(1+i)/(1+g) i’=(i-g)/(1+g)
so A/i’ = A x (1+g)/(i-g) not (A/(i-g))
Future value of a present sum
The future value (FV) formula is similar and uses the same variables.
Future value of an annuity
The future value of an annuity (FVA) formula has four variables, each of which can be solved for:
1. FV(A) is the value of the annuity at time = n
2. A is the value of the individual payments in each compounding period
3. i is the interest rate that would be compounded for each period of time
4. n is the number of payment periods
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