FV

Returns the future value of an initial sum with a subsequent stream of payments.

Syntax:

FV(rate, numperiods, payment, presentvalue, type)

rate: the (fixed) interest rate per period.

numperiods: the total number of payment periods in the term.

payment: the payment made each period. If presentvalue is given, this may omitted (defaults to 0).

presentvalue: the lump sum payment at the start of the term (optional - defaults to 0). With a loan, this would normally be the sum borrowed; with a bond this would generally be 0.

type: when payments are made (optional - defaults to 0):

0 - at the end of each period.

1 - at the start of each period (including a payment at the start of the term).

The value of money is time-dependent; for example, $100 today would be worth $110 in a year if invested at a 10% interest rate.

FV returns the future value at the end of the term, of a lump sum payment (presentvalue) at the start of the term and a payment being made each period for numperiods periods, at fixed rate interest, compounded each period.

Example:

FV(5%, 3, -1000, 0, 0)

returns a future value of 3,152.50 in currency units. You pay 1,000 at the end of each year for 3 years. Assuming an interest rate of 5% you expect to receive 3,152.50 at the end of the term. 1,000 is negative because you pay it. The future value is positive because you receive it.

FV(7%, 10, -1400, 10000, 0)

returns a future value of -328.49 in currency units. You borrow 10,000 at an interest rate of 7% and pay 1,400 at the end of each year for 10 years. 10,000 is positive because you have it. 1,400 is negative because you pay it. The future value is negative because this is the amount of money you owe at the end of the term.

FV(7%, 1, 0, 10000, 0)

returns a future value of -10,700 in currency units. You borrow 10,000 at an interest rate of 7% and don't pay any of it back. After 1 year you owe 10,700.

Application:

Imagine you have an initial savings of $5,000 and you plan to invest it in a mutual fund that is expected to have an average annual return of 8%. Additionally, you decide to make a regular contribution of $200 at the end of each month. You want to know how much your investment will be worth in 10 years.

Here's how the FV function would be applied:

Rate (interest rate per period): Since the annual return is 8% and the contributions are monthly, the rate per period is 8% / 12 = 0.67% or 0.0067.
Nper (total number of payment periods): The investment duration is 10 years, with monthly contributions, so the number of periods is 10 * 12 = 120.
Pmt (payment made each period): This is the monthly contribution of $200.
Pv (present value or initial investment): This is your initial savings of $5,000.
Type (when payments are due): Payments are made at the end of the month, so the type is 0.

The formula would be:

FV(rate, nper, pmt, pv, type)

FV(0.0067, 120, -200, -5000, 0)

Note: The Pmt and Pv values are entered as negative numbers because they represent cash outflows (money leaving your pocket).

The result of this calculation would be approximately $47,813.35.

Table Breakdown

	Variable	Description	Value
	A	B	C
1	Rate	Annual interest rate (8%) divided by 12 months	0.006666667
2	Nper	Number of years (10) multiplied by 12 months	120
3	Pmt	Monthly payment	-$200.00
4	Pv	Initial investment	-$5,000.00
5	Type	Payments are at the end of the period	0
6	FV	Future Value	$47,813.35