# Documentation/How Tos/Calc: PV function

CALC FUNCTIONS
FUNCTIONS
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Payment Streams, Annuities, Loans
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## PV

Returns the present value of a stream of future payments with a final lump sum.

### Syntax:

PV(rate; numperiods; payment; futurevalue; 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 futurevalue is given, this may omitted (defaults to 0).
futurevalue: the cash balance you wish to attain at the end of the term (optional - defaults to 0). With a loan, this would normally be 0; with a bond this would be the redemption value.
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.
PV returns the value today, of a payment being made each period for numperiods periods, with an additional lump sum payment (futurevalue) at the end of the term, at fixed rate interest, compounded each period.
The examples below clarify how the function may be used.
See Derivation of Financial Formulas for the underlying formula.

### Example:

PV(5%; 15; 1000; 0; 0)

returns -10,379.66 in currency units. You have the opportunity to buy an annuity, which would pay you 1000 at the end of each year for 15 years. You assume a constant interest rate of 5%. On this basis, the annuity is worth 10,379.66 today; if it is priced higher than this you might not wish to buy it. The result is negative, because you must pay for the annuity.

PV(5%/12; 3*12; -100; 0; 0)

returns 3,336.57 in currency units. You are considering a loan of 3,500, which would mean you paying back 100 at the end of each month for 3 years. You assume a constant interest rate of 5%. On this basis, the loan is only worth 3,336.57, so might be a poor deal. The monthly payment is negative because you pay it, and the result positive because the loan is paid to you.

PV(7%/2; 3*2; 100; 1000; 0)

returns -1,346.36 in currency units. A 3 year bond is issued, paying 100 currency units semiannual coupons and 1000 currency units on maturity. You require an annual rate of return of 7% (compounded semiannually) bearing in mind any risk, and hence you value the bond on issue at 1,346.36. The result is shown as negative, as you would have to pay for the bond.

### Issues:

• Take care that you understand how this function compounds the interest each period. Many financial calculators allow you to set a separate compounding period - spreadsheets do not. Choose the interest rate appropriately.