# Present today is worth more at the end

Present value of an ordinary annuity: the present
value of an annuity Refers to the value at the beginning of the term of an
annuity which is known as period 0 which is equitant to future cash flows
discounted at the same rate of interest. Due to the time value of money concept
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 each annuity payment, 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 an annuity due: annuity due means
that 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. Annuity due payments are
made is made in before receiving a service, but an ordinary annuity payment is
made after revving the service. Annuity due may 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. Since an annuity due payments reflect number of
future cash inflows, the one making the payment may which to calcite the value
of the annuity while accounting the time value of money.

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Future value of an annuity due: the future value
of an annuity due calculates the value of money at a future date. The
difference between a present values of annuity due a future value of annuity
due is simple. Let’s say that someone or a company want to invest an annuity
from a client and the first payment of that is received when that annuity was
acquired. If a client is wanting to calculate what their balance would be after
a few years in an interest account they would choose to put the first cash flow
immediately into the account, in this situation we have to use the future value
of an annuity due formula. FVAD= PVA (1+I).

Investing: there are many
types of investments that can be made but the focus here is only two. Those two
are stocks and bonds. Stakeholders have a claim on the company’s assets because
they own part of their stocks. The holders of stock can’t vote off the
president of the company but can call him or her and find out what types of
problems are going on and why. Bonds is where an investor is loaning their
money to a company plus the return of the bonds face amount when the bond
eventually matures.

Perpetuity: if an annuity goes on forever then it is
called perpetuity. It is constant stream of cash flows that have no end. In
perpetuity the beholder is entitled to receive annual interest payments
forever. Because of Time Value of money each payment is only a fraction of the
last payment. The difference between an annuity and propriety is that prosperity
is a type of annuity that goes on forever. A person might use the property
formula to calculate that amount of cash flow in the current year. The
eprupuity formula is sued to calculate an eprupuity of cash flow divided by
discount rate. The formula for perpetuity is PV= PMT/ I which is interest. However
if the payments grow at a constant rate then it is a growing prepuaity. A growing perpetuity is a series pf periodic
payments that grow and are received for an eternal amount of time. This is used
real state especially because over time the cash flow with grow over time.

NPV:
Until this point the main focus has been annuities and perpetuity however that
is only using even cash flows, however there are other situations that require
the use of unequal cash flows. A perfect example of that would be picking one
business deal over the other. One way to do this for every single project is to
calculate the net present value of each cash flow of each project do determine
which project is the better one to go with. 