# Periodic an amortized loan would be a car

Periodic interest rate: the periodic
interest rate is the interest rate
charged on a loan or realized on an investment over s specific period of time.
In most cases interest compounds more than an annual compound. For
clarification purposes let’s say that we have an annual interest rate of 10%,
the periodic interest rate would be 0.10/12 which would equal to 0.83 or 83%.
That means that every months the remaining principal balance of a loan has
0.83% interest applied to it. It is important to remember that number of
compounding periods has a huge effect on the epidotic interest rate of an
investment. Let’s say an investment has an effective annual interest of 12%,
and it compounds every month, its periodic interest rate is 1%. Let’s say if it
compounds weekly then it would be 14 percent.

Loan
Amortization:
A loan amortization is a type of loan that has scheduled periodic payments that
consist of both Principal and Interest. In n amortized loan a payment pays
interest for the period before the principal is paid and eventually reduced. A
great example of an amortized loan would be a car payment, or even a house
payment. Now the two important factors of it are the principal and the
interest. Since interest is calculated based on the very recent ending balance
of the loan, that option of loan payment decreases as more and more payments
are made. Overall the balance reduces each time the principal goes down.

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Continuous
compounding: this
is an extreme case for compounding since almost all interests are compounded
either monthly, quarterly, or
semiannually.  Instead of using finite number to calcite
interest rate, continuous compounding completes interest thinking that there
will always be computing over an infinite number of years. Even with major
investments, the difference with interest earned through this method is not
very different form the traditional compounding model. There formula for this
compounding if it is present value is PV= FV (e^it).

Now let’s say I invest 300 dollars at 10% forever
compounded for 3 years. How much will I have after those three years? In order
to compute that we have to use the formula known as PV= FV. E^it we would have
PV= 300(E^0.30) =404.96

However that is under the simple interest,
now if we assume that we are dealing with compound interest. For example let’s say we want to know the
future value of 10 dollars invested for 50 years at 5%. Even though using
the calcactor would be easier and less time consuming that will not be
necessary currently because these numbers are small and easy to work with. The formula would be FV= PV(1+I)^n= 10(
1.05)^50= 114.67.

0    1    2
3     4            50

Pv                                 FV

I want to know if I want to have 5,000\$
after 20 years, how much should I deposit today if the interest is 12%. Since
the numbers are getting bigger we will need to solve it by imputing numbers
into the finical calculator. -5,000 PV, 20 N, 12 I/Y and then CPT FV then we
get 48,231.47 dollars. This means that if we invest 5,000 with a 12% interest
then after 20 years we would have 48,231.47 which is rare. The reason why 5,000
was put in negative was because I am taking 5,000 dollars out of my pocket and
then investing it.

0
1    2      3
4     5     6
21

-5,000                                         I/Y 12%

Now using Annuity if we deposit 500 dollars per year for 5 years at 6%
then how much will we have after 5 years? We would input -500 PMT, 5N, 6 I/Y
then CPT FV which would be 2,818.55. that means that we have after 5 years of
investing 500 dollars making 6% interest.

0      1
2    3         4
5

-500 -500 -500 -500 -500    I/Y 6

Now if we want to know the present value
of the annuity which would tell us how much should we invest today in order to
windflaw 600 dollars for the next 5 years? Using the incisal calculator we
would input 600 PMT, 6 I/Y, 5N then hit CPT PV – 3,633.36.

Now let’s say I had the choice between two
project’s to invest in. let’s say project A offered me an annuity at 20,000 and
receive 2,000 for 15 years. -20,000 PV, 2,000 for PMT, 15N then CPT I/Y=
5.56.Then lets say the project B gives me the same amount buy has interest of
6%. In that case project A is preferred over Project B because A has less
interest than B.

PV
example: for
example let’s say I wanted to know the present value of 5 year annuity due of
200 payments at 5%. This would be solving by plugging in 5N, 200 PMT, 5% I/Y
CPT PV 865.90. Now that we have that we will have to use the formula PVAD= PVA
(1+I). Using that we would have PVAD= 865.90(1.05) = 909.20

Now let’s say I wanted to know the FV of a
4 year annuity due of 150 dollars payments at 12%

Then we would first put in 4N, 150 PMT,
12% then hit CPT FV which equals 716.90 then would find the FVAD which equals
716.90(1.12)= 802.93.

Now it’s time to calculate what happens if
an annuity goes forever. By using the formula PV=PMT/I we can calculate the
perpetuity. For example if we invest into an account 10% and receive 250
dollars every year forever then we have to divide 250/0.1= 2,500. However this
does not show what happens if the market goes into problems like inflation or
recession. In order to figure out what happens then we would have to use the
Growing perpetuity formula which is PV= PMT/I-G.

For example if we have 5% interest but our
growth rate is 2% then the present value of the growing perpetuity has to be
PV= 250/0.05-0.02=8,333.33 that is true because over time the cost of living
grows and everything eventually increase in cost therefore 2,000 without
interest would be worthless in 20 years since it would remain the same.

Project A                0            1          2        3        4         5

300     100
400    200     600
900             I/Y= 12

Project B              400     200
300   200      500
700

In order to correctly choose which one
would be better for the company to take if we use the finical calculator it
would be very simple to figure out what the Net Present Value would be. That
would be done by first going to CF and then entering data for each project and
after that we would hit CPT NPV for both project and then we figure out which
one would be the better option. For PA the NPV would be 308.33 while for PB it
would be 408.33. usually people would defiantly pick the second project because
it brings back more at an earlier time, however when all is said and done it is
up to the manger which project he or she would think is best for the long term
and by computing the NPV they would have a good idea as to where they should
direct their investment in.

Now if I a company wants to know that they
needed to borrow 100,000 at 10% for 25 years, making semiannual payments. The
question would be how much would their first payment has to be. By using the
financial calculator the first payment would be PV=100,000, I/Y= 5 because it
is an semiannual payment and N= 50 and then CPT PMT. The answer would be
5,477.67. That payment stays the same throughout the entire loan however the
interest does change. By setting up an Amortization table we can figure out how
each payments interest is.

P      BEG BALANCE         PMT             INT          PR         END BALANCE

1        100,000                      5,477.67       5,000
477.67     99,522.33

2         99,552.33                  5,477.67       4,976.12   501.55
99,050.78

3         99,050.78                  5,477.67      4,952.54
525.13     98,525.65

4         98,525.65                  5,477.67       4,976.28   551.39
97,974.29

This table shows us each payment connects to
its interest and how much it applies to principal. It gives us ending balance
for each period. It is quite simply the first thing to do is to calculate the
interest which would be done by multiplying the beg balance by the interest
rate, then to calculate the PR we would subtract interest form the payment.
Then finally the ending balance is calculated by subtracting PR from the
beginning balance.

Continuous compounding Now let’s say I
invest 300 dollars at 10% forever compounded for 3 years. How much will I have
after those three years? In order to compute that we have to use the formula
known as PV= FV. E^it we would have PV= 300(E^0.30) =404.96