# Pv

## Pv(rate, nper, pmt*, fv, type*)

Returns the present value of an annuity in which you receive (or pay) a constant amount each period for a fixed number of periods, and then receive (or pay) a lump sum after the final payment. The result is positive if you would receive money in exchange for the annuity (for example, if you receive a loan). The result is negative if you would have to pay money to acquire the annuity.

Parameters:

- «Rate»
- Interest rate per period.
- «Nper»
- Total number of periods for the annuity.
- «Pmt»
- Payment made each period.
- If you make payments, like paying a loan, this is a negative number.
- If you receive payments, this is a positive number.
- «Fv»
- (Optional) The balance remaining at the end after the last payment is received.
- If you make payments, a negative number indicates the required balloon payment at the end of the loan.
- If you receive payments, a positive
- «Type»
- (Optional) Indicates whether payments are at the beginning of the period.
`True`

= Payments due at beginning of period, with first payment due immediately.`False`

= Payments due at end of period. (default)

## Library

Financial Function

## Examples

A lottery winning pays $50,000 per year for 15 years, with the first payment occurring immediately. Following the last payment, there is a final lump-sum payment of $250,000. Assuming an 8% return, this "million dollar" prize is really worth:

`-Pv(8%, 15, 50000, 250000, 1) → $541,022.28`

Note that the result of Pv is negative since you would have to pay money to acquire the equivalent of the lottery's future payments.

You are considering the purchase of an annuity that pays $500 per month for 10 years, with the first payment occurring at the end of the first month. With a 6% annual yield (0.5% monthly), the value of this annuity is:

`-Pv(0.5%, 12*10, 500) → $45036.73`

You can afford $1500 per month on mortgage payments, and are considering a 30 year fixed rate loan at .565% per month (= 7% APR). The size mortgage that you can afford is given by:

`Pv(0.565%, 30*12, -1500) → $230558.71`

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