# Future Value of Cash Flows Calculator

## Calculator Use

Calculate the future value of a series of cash flows. More specifically, you can calculate the
**future value of uneven cash flows** (or even cash flows).

- Interest Rate (discount rate per period)
- This is your expected rate of return on the cash flows for the length of one period.
- Compounding
- If there is compounding, this is number of times compounding will occur during a period. 1 is the minimum.
- Cash Flows at Period Beginning or End
- Choose whether cash flows occur at the beginning of each period (like an annuity due; in advance) or at the end of each period (like an ordinary annuity; in arrears)
- Periods
- This is the frequency of the corresponding cash flow. These are often the equivalent time period of months or years but a period can be any repeating time unit that payments are made.
- Cash Flows
- The cash flow (payment or receipt) made for a given period or set of periods.

## Future Value of Cash Flow Formulas

The future value, FV, of a series of cash flows is the future value, at future time N (total periods in the future), of the sum of the future values of all cash flows, CF.

We start with the formula for FV of a present value (PV) single lump sum at time n and interest rate i,

Substituting cash flow for time period n (CF_{n}) for
PV, interest rate for the same period (i_{n}), we calculate future value for the cash flow for that one period (FV_{n}),

If our total number of periods is N, the equation for the future value of the cash flow series is the summation of individual cash flows:

For example, i = 4% = 0.04, compounding once per period, for period n = 5, CF = 500 at the end of each period, for a total number of periods of 7,

Therefore,

FV_{5} = CF_{5} * (1 + i_{n})^{7-5 }

FV_{5} = 500 * (1 + 0.04)^{2 }

FV_{5} = 500 * (1.04)^{2 }

FV_{5} = 500 * 1.0816

FV_{5} = 540.80

When cash flows are at the beginning of each period there is an additional period required to bring the value forward to a future value. Therefore, an additional (1 + i_{n}) is present in each cash flow multiplication.

With compounding m times per period we arrive at i_{n} and n by setting r as the periodic rate and t as the period number to calculate i_{n} = r/m and n = mt; we can now calculate the
PV starting with the future value formula

Calculating the FV for each cash flow in each period you can produce the following table and sum up the individual cash flows to get your final answer. Note that since we want to know the future value at the end of the 7th period, the future value is unchanged from the cash flow of $700.

**2,945.61**