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Future value is the value of an asset at a specific date. [1] It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function. [2]
The present value of $1,000, 100 years into the future. Curves represent constant discount rates of 2%, 3%, 5%, and 7%. The time value of money refers to the fact that there is normally a greater benefit to receiving a sum of money now rather than an identical sum later.
Thus the discounted present value (for one cash flow in one future period) is expressed as: = (+) where DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the delay in receipt; FV is the nominal value of a cash flow amount in a future period (see Mid-year adjustment);
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, () is the exposure at time , and (,) is the risk neutral probability of counterparty default between times and .
The present value (today) of a payment of 1 that is to be made years in the future is (). This is analogous to the formula (+) for the future (or accumulated) value years in the future of an amount of 1 invested today.
The D factor is for discounting, because the expiration date is in future, and removing it changes present value to future value (value at expiry). Thus N ( d + ) F {\displaystyle N(d_{+})~F} is the future value of an asset-or-nothing call and N ( d − ) K {\displaystyle N(d_{-})~K} is the future value of a cash-or-nothing call.
It compares the present value of money today to the present value of money in the future, taking inflation and returns into account. The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs a present value, which is the current fair price .
Present value calculations, and similarly future value calculations, are used to value loans, mortgages, annuities, sinking funds, perpetuities, bonds, and more. These calculations are used to make comparisons between cash flows that don’t occur at simultaneous times, [ 1 ] since time and dates must be consistent in order to make comparisons ...