Periodic interest rate: the periodicinterest rate is the interest ratecharged on a loan or realized on an investment over s specific period of time.In most cases interest compounds more than an annual compound. Forclarification 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 has0.
83% interest applied to it. It is important to remember that number ofcompounding periods has a huge effect on the epidotic interest rate of aninvestment. 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 itcompounds weekly then it would be 14 percent. LoanAmortization:A loan amortization is a type of loan that has scheduled periodic payments thatconsist of both Principal and Interest. In n amortized loan a payment paysinterest for the period before the principal is paid and eventually reduced. Agreat example of an amortized loan would be a car payment, or even a housepayment.
Now the two important factors of it are the principal and theinterest. Since interest is calculated based on the very recent ending balanceof the loan, that option of loan payment decreases as more and more paymentsare made. Overall the balance reduces each time the principal goes down. Continuouscompounding: thisis an extreme case for compounding since almost all interests are compoundedeither monthly, quarterly, orsemiannually. Instead of using finite number to calciteinterest rate, continuous compounding completes interest thinking that therewill always be computing over an infinite number of years. Even with majorinvestments, the difference with interest earned through this method is notvery different form the traditional compounding model. There formula for thiscompounding if it is present value is PV= FV (e^it). Now let’s say I invest 300 dollars at 10% forevercompounded for 3 years.
How much will I have after those three years? In orderto compute that we have to use the formula known as PV= FV. E^it we would havePV= 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 thefuture value of 10 dollars invested for 50 years at 5%. Even though usingthe calcactor would be easier and less time consuming that will not benecessary 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 FVI want to know if I want to have 5,000$after 20 years, how much should I deposit today if the interest is 12%. Sincethe numbers are getting bigger we will need to solve it by imputing numbersinto the finical calculator. -5,000 PV, 20 N, 12 I/Y and then CPT FV then weget 48,231.
47 dollars. This means that if we invest 5,000 with a 12% interestthen after 20 years we would have 48,231.47 which is rare. The reason why 5,000was put in negative was because I am taking 5,000 dollars out of my pocket andthen 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/Ythen CPT FV which would be 2,818.55. that means that we have after 5 years ofinvesting 500 dollars making 6% interest.0 1 2 3 4 5 -500 -500 -500 -500 -500 I/Y 6Now if we want to know the present valueof the annuity which would tell us how much should we invest today in order towindflaw 600 dollars for the next 5 years? Using the incisal calculator wewould input 600 PMT, 6 I/Y, 5N then hit CPT PV – 3,633.36.
Now let’s say I had the choice between twoproject’s to invest in. let’s say project A offered me an annuity at 20,000 andreceive 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 of6%. In that case project A is preferred over Project B because A has lessinterest than B. PVexample: forexample let’s say I wanted to know the present value of 5 year annuity due of200 payments at 5%. This would be solving by plugging in 5N, 200 PMT, 5% I/YCPT 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) = 909.20Now let’s say I wanted to know the FV of a4 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 equals716.
90(1.12)= 802.93. Now it’s time to calculate what happens ifan annuity goes forever. By using the formula PV=PMT/I we can calculate theperpetuity.
For example if we invest into an account 10% and receive 250dollars every year forever then we have to divide 250/0.1= 2,500. However thisdoes not show what happens if the market goes into problems like inflation orrecession. In order to figure out what happens then we would have to use theGrowing perpetuity formula which is PV= PMT/I-G. For example if we have 5% interest but ourgrowth rate is 2% then the present value of the growing perpetuity has to bePV= 250/0.05-0.02=8,333.33 that is true because over time the cost of livinggrows and everything eventually increase in cost therefore 2,000 withoutinterest 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 onewould be better for the company to take if we use the finical calculator itwould be very simple to figure out what the Net Present Value would be. Thatwould be done by first going to CF and then entering data for each project andafter that we would hit CPT NPV for both project and then we figure out whichone would be the better option. For PA the NPV would be 308.33 while for PB itwould be 408.33. usually people would defiantly pick the second project becauseit brings back more at an earlier time, however when all is said and done it isup to the manger which project he or she would think is best for the long termand by computing the NPV they would have a good idea as to where they shoulddirect their investment in.
Now if I a company wants to know that theyneeded to borrow 100,000 at 10% for 25 years, making semiannual payments. Thequestion would be how much would their first payment has to be. By using thefinancial calculator the first payment would be PV=100,000, I/Y= 5 because itis an semiannual payment and N= 50 and then CPT PMT. The answer would be5,477.67. That payment stays the same throughout the entire loan however theinterest does change.
By setting up an Amortization table we can figure out howeach 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 toits interest and how much it applies to principal.
It gives us ending balancefor each period. It is quite simply the first thing to do is to calculate theinterest which would be done by multiplying the beg balance by the interestrate, then to calculate the PR we would subtract interest form the payment.Then finally the ending balance is calculated by subtracting PR from thebeginning balance. Continuous compounding Now let’s say Iinvest 300 dollars at 10% forever compounded for 3 years. How much will I haveafter those three years? In order to compute that we have to use the formulaknown as PV= FV. E^it we would have PV= 300(E^0.30) =404.96