Engineering Economic Analysis - Simple Interest Rate - YouTube

Hello everyone. In this video we're going to talk about time value of money, which

is the basis of engineering economic analysis. So let me start

by asking you these two questions. The first one is, would you rather receive

$1000 today or $1000 a year from today. I'm guessing

you would rather have $1000 today? And the answer, the reason is

because in the mean time, in the next year, you could increase the value of

$1000 by simply putting it in a savings account, and you

know, earning interest on that. So that's why you're probably going with that

option. But the second question is asking, would you rather receive $1000

today or $2000 a year from today? Well, this is a different

question. Now you have to think about, is that additional $1000 that

you're receiving if you wait for another year, is enough for you? Is that

representing your time value of money or not. And, you know, I'm, quite frankly

really depends on how greedy you are. I would probably go with the $2000

a year from today because in a year I'm doubling that amount. That

basically means 100% return. So let's put everything into perspective.

What we're doing here by asking these questions is, we can realize that money

can be essentially rented in roughly the same way that one rents an apartment.

When we are renting an apartment, we're essentially giving that space and we're

charging money, and at the end of the period, we're getting the space back. So

the rent is an analogy for the interest rate when you're renting your money.

Money has earning power, and if you own money and someone needs it, you can loan

it to them and charge them interest. The interest rate you charge them

is based on your time value of money. So there is an interest rate here that

represents your time value of money. In this case, the interest rate or the time

value of money was 100% because you're doubling the amount. So the time, the

value of a given sum of money does not only depend on the amount of money, it

also depends on the point in time. Where, when exactly do you have that money. Not

only the amount but also the time. And that's the point behind, quite frankly,

this course. Time value of money is calculated using an interest rate. An

interest rate, you can see that it is also called discount rate, sometimes minimum

attractive rate of return, MARR, or cost of capital. Let's look at this example

here and put everything in perspective. A man borrowed $1,000 from a bank and 8%.

He agreed to repay the loan in two end-of-year payments. At the end of each year,

the interest that is due. Compute the borrower's cash flow. So let's start by

drawing the cash flow here. Cash flow diagram at time 0 from the

perspective of this man is receiving $1000, okay. And we have here

1, we have here 2. And what we want to compute here is how much he needs

to repay at the end of each year. So at the end of year 1, he will repay half

of the principal. So it is $500 plus the interest that is due.

So plus some amount and that amount is the interest on $1000. An

interest rate is 8% yearly so that means 8% times the money

that he borrowed for that year. So that is equal to 500 + $80, so $580 is what he

will repay at the end of year 1. But what happens at the end of year 2 is that he

will pay another half of the principal another $500, and then the interest of the

money that he borrowed for the second year. For the second year, he's again paying

8% interest so 8% interest. And the money that he borrowed in that time

frame, he is borrowing $500 because he paid off the first $500.

So, 8% times $500, so he's paying back $540. So $540 and $580 is what he will

be repaying year 2 and year 1. So this is the cash flow of this problem. So if

you were to loan a present sum of money P to someone in a simple interest rate

of I for a period of n years, the total interest that you will basically earn is

the sum of money that you're lending times the interest rate - your time value

of money - times the duration of that - which is P times I times N. And the money

that you would end up with at the end of the period is your present sum that

you add plus the interest that you earned. So P plus Pin.

The important definition here is the simple interest

definition, and that is the interest on the original sum only. And it's a very

important point because later on we'll be talking about compound interest and

that is the main difference between simple interest and compound interest.

Simple interest is only on the original sum of money and not accrued

interest. Let's look at another example here. You have agreed to loan a friend

$5000 for 5 years at a simple interest rate of 8% per

year. How much interest will you receive from the loan?

How much will your friend pay you at the end of 5 years? So again, in any

problem, let's start always with drawing a cash flow diagram. In this case it's a

very simple one times zero. You know, from your perspective, you are giving away

$5000, and at the end of year 5, you're getting something back.

We want to compute that here. So our P here is $5000.

Number of years n is 5 years. Interest rate is 8%. The total

interest, to answer the first part of the problem, how much interest will receive

from the loan. The total interest

will be Pin. Remember that, Pin. So $5000 times 8% and times 5 years.

So you will receive $2000 in interest. And the total money that you

would collect here at the end of year 5 will be your principal. Principal

plus interest. So your principal was $5000 plus the

$2000 interest. You will receive $7000. That's

how simple interest works, and it's pretty simple. In the next video we'll be

talking about compound interest rate.