# Present sum of money given a specific rate

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Last updated: May 16, 2019

Present value of money: in any investment project involves the exchange of present money for some offer of future money. To relate back to the future value of money the future dollars has to be discounted to the present value for the interest rate of the firm decides on all of its investment projects. This concept means that the current worth of a future sum of money given a specific rate of return. Future cash flows can be discounted at the discount rate, which means the higher the discount rate, the lower the present value of future cash flow. It is very important to determine correct discount rate which is key for ovulating future cash flow.

you received 100 today, the present value of this would be 100 dollars because this investment was given to you today. however if you received the same 100 dollars in two years, the present value would not be 100 dollars because it was not given to you right now. In order to find the PV of that 100 dollars, we need to find out how much is needed to be invested today in order to receive that 100 dollars sometimes in the future. The formula for this would be FV=PV*(1+I) 6N.

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n order to clause the present value or the amount that must be invested today, we have to subtract the interest form the 100 dollars, in order to do that we can discount future payments by the interest rate for the entire period. Present value of an ordinary annuity: the PV of an annuity is at the beginning a term of annuity which is known as period 0 to future cash flows. Because of TVM receiving the money today makes more sense than receiving the money of the future because money today is worth more than money in the future. If we continue by that logic receiving 100 dollars today is worth more than remaining 20 dollars over the course of five years.

The amount of money investment today is worth more at the end of five years than simple investment of 20 dollars each. Hence we have PVA= PMT 1-1/1+I^)N/I. p means the present value of an annuity, PMT is the dollar amount of evert signe  annuity, I means the interest rate which is also known as the discount rate, and n is the number of periods in which the payments are made.   Present value of annuity due: annuity due is an annuity whose payment is to be made instantly at the beginning of every period.

A good example of an annuity due is rent because that payment is maid at the start of ever new month which different form having the rent collected at the end of the month which would be ordinary annuity. AD payments are made is made in before receiving a service, but an ordinary annuity payment is made after revving the service. AD happen in some form as a bill, rent, and even cellphone payments because those payments have to be made at the beginning of very period. annuity due payments reflect number of future cash inflows, the one making the payment calcuates the value of the annuity while accounting the time value of money.

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