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Drift Flux Model — Transcript · YTtoTranscript

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Drift Flux Model

Engineering Economic Analysis · 1,695 words · 8 min read · EN-ORIG

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welcome to the lecture on interest formulas so in this lecture we will discuss about the discrete compounding discrete payments in that we will come across certain symbols what does these symbols mean so in these symbols you have i n p a and F where I is the annual interest

rate and the n is number of Interest

periods then p is present amount at the beginning a whenever we will discuss this will be equal annual payment

made at the end of the

year F will be the final amount or compounded amount so we will have certain points to remember that we will be following the concept that end of one year is beginning of the next year so if a payment is made at the end of the year it means the same amount will be at the

beginning of the next year p means beginning of a year that is present time at zero time f is at the end of n year now occurrence of a so what does it mean when a and P are involved so when A and P are involved if we see at zero time a starts from one

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year so every year end you are paying certain amount a

When A and P is involved P occurs at the beginning time so this is when A and P is

involved P represents the amount 1 year earlier to first time a occurs when a and F is involved in that case a starts from the first year as usual

and F will be matching with the last a so when a and F are involved

last a will coincide with F this represents the fact that you are starting the payment the equal annual payment at the end of first year and it goes till the end of the nth period P represents here at the initial point and F represents at the last time now we have to discuss two types of

factors one is single payment compound amount factor and another is single payment present worth Factor we will discuss what are these factors single payment compound amount

Factor this is a factor as the name indicates it is a factor this Factor also is represented by F by p i n now what is this Factor this is a factor which when multiplied with the present amount it will give you the future amount at some future time when multiplied with present amount

will give you compound

amount and interest periods hence how you can find this Factor so suppose you have here one 2 3 2 N you have amount at the beginning of

year you have interest earned during year

and you have compound amount at end of year so if you have a present amount of p and in interest rate is I and there are are n interest periods so during the first year the interest which will be earned will be P * I so your compound amount at the end of

year 1 will be p + P into I that is p into 1 + I at the end of 2 year in the second year your amount is now P into 1 + I because it's a case of compound interest so your amount which is at the beginning of year 2 is p into 1 + I now

interest will be on this amount so this will be P into 1 + I * I so so if you add these two it will give you the compound amount at the end of year two so if you add them P into 1 + i+ P into 1 + I into I that is p into 1

+ I to the^ 2 in the beginning of the third year you have P into 1 + I to ^ 2 again you have interest aced as P into 1 + I ^ 2 * I so it will come out to be P into 1 + I to^ 2 into I + P into 1 + I ra to the ^

2 that is p into 1 + I ra to the ^ 3 so what we see at the end of in the during the N year at the begin meaning the amount which is owed is p into 1 + I to the power ra to the^ n minus 1 and your interest will be P 1 + I ra to the ^

nus1 into I and your final amount comes out to be P into 1 + I ra to the power n so this is nothing but the amount which will be paid by the borrower now this is the factor 1 + I raised to the power n which is Multiplied with the principal amount and it gives you the

final amount the final compound amount so that is why this Factor 1 + I ra to the power n this is known as single payment compound amount Factor so 1 + I ra to the power n is single payment compound amount

factor and it is represented by a symbol that we will be practicing during the course this is represented by a symbol F by p i n means this factor F by P once is it is Multiplied with P this p and p will cancel and you will get F so this is single

payment compound amount factor F by P I N let us see by an example this Factor will be useful for the calculations in the cases when an investor has to find that if he invest invests certain amount now what he will be getting at the end of certain interest periods so suppose an

investor an investor wishes to know how much he will get if he invests now rupees 10,000 for 4 years at 16% annual interest rate so for these cases you are given that the presently the investor is investing 10,000 so p is rupees 10,000 I is 16% and N is four so basically P should be multiplied

with single payment compound amount Factor

that is f by P rate of interest is 16 and four so and this Factor value of this factor is 1 + 0.16 to the ^ 4 that is 1.81 1 means if the present amount is Multiplied with this Factor it will give him the amount which he will receive at the end of four years so P multiplied by

F by P 164 will be f it means F will be 10,000 multiplied by 1. 1811 that comes out to be 18110 now we are calculating this because it's a simple calculation but we have the tables supplied for this type of discrete compounding discret payment for a particular interest rate and we can refer this

values value of these factors which is provided at the end of the book and directly you can get these factors and find the value of f so this is how we calculate the single payment compound amount Factor we try to calculate the value of compound amount at the end of certain interest periods the next is

single payment present worth Factor single payment present worth

Factor just opposite to the single payment compound amount Factor we have single payment present worth Factor it is a factor it is a factor which when multiplied with some future amount will give us the present

amount for the investment so as we have seen that in the earlier case a factor when multiplied with P gives you f in this case it is a factor which when multiplied with f will give you P so supp an investor wants to know that how much he should invest now so that he can get

18110 at the end of 4 years that was the earlier case now the investor wants to know that he will get 18110 at the end of four years how much he should invest now so in that case he has to so if investor wishes to know how much he should invest now to

get 18110 rupees 18110 H for years hence at interest rate of 16% per enom in that case a factor should be there which should be multiplied with the F and that should give him the present amount so that factor is p by f i n so in this case you will have P by f i n

that is nothing but P by F 164 this factor is basically the reciprocal of the single payment compound amount Factor this factor is reciprocal of single payment compound amount

Factor so P by f i n you can write it as 1 by 1 + I ra to the power n and this Factor is known as single payment present worth Factor because this Factor when it is Multiplied with f it gives you the present amount so in the present case when your f is given as

18110 and I is 16% n is 4 so F by P by f i n 164 will be equal to 1 by 1.16 to the^ 4 so you can calculate p as 18110 multiplied by 1 by 1.16 ra to the power 4 and this comes out to be 10,000 so what we see that this is a

factor which when multiplied with the future amount it gives you the present amount so that is why it is known as single payment present worth factor in a nut cell also they are called as C f as well as pwf so this single payment present worth Factor many a times you will see

it as pwf means present worth factor and similarly single payment compound amount factor is CAF so CAF means single payment compound amount Factor

so this is how once you know the factor values you can find the values of P or F either at the present time or at some future time thank you [Music] oh [Music] [Music]

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