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.

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