So allow” s generalize a little bit
Let” s claim I ‘ m. loaning P bucks. P dollars, that ‘ s what I.
borrowed obtained that” s my initial first.
r is equal to the price,. the rates of interest that I ‘ m loaning at.
And I ‘ m going to
borrow. Let ‘ s see if we can come up. Allow” s do basic.
because that” s basic. At time 0– so allow” s make. this the moment axis– just how much am I mosting likely to owe? Well, that” s right when I.
obtain it, so if I paid it back immediately, I.
would simply owe P, right? Sometimes 1, I owe P plus the.
passion, plus you can kind of view it as the rental fee on that particular.
cash, and that” s r times P.And that previously, in the.
previous example, in the previous video, was 10%. P was 100, so I had to pay $10.
to borrow that money for a year, and I had to.
pay back $110. And this coincides thing.
As P times 1 plus r? Because you could.
simply utilize 1P plus rP. And after that after 2 years,.
just how much do we owe? Well, yearly, we simply.
Pay an additional rP? In the previous instance,.
it was another $10.
So if this is 10%, every.
year we just pay 10% of our original principal. So in year 2, we owe P plus.
rP– that” s what we owed in year 1– and after that another.
rP, so that equates to P plus 1 plus 2r. And just take the P out,.
and you get a 1 plus r plus r, so 1 plus 2r. And afterwards in year 3, we” d owe. what we owed in year 2.
So P plus rP plus rP, and after that. we simply pay an additional rP, another say, you recognize, if r is 10 %, or.
50% of our initial principal, plus rP, and so that. equals P times 1 plus 3r.’So after t years,.
just how much do we owe? Well, it” s our initial. principal times 1 plus, and
it ‘ ll be tr. So you can disperse this out. And
there ‘ s going since every year we pay Public relations. to be t’years.
Therefore that ‘ s why. it makes good sense. So if I’were to say. I ‘ m borrowing– let ‘ s do some numbers. You could function it out in this manner,. and I suggest you’do it.You shouldn ‘
t simply. memorize solutions. If I were to borrow $50 at 15%.
Time 20 times 0.15? That ‘ s 3? It ‘ s 50 times 4, which.
is equivalent to $200 to obtain it for 20 years.
So $50 at 15% for 20.
years results in a$ 200 payment at the end.So this was simple. interest, and this was the formula for it. Allow ‘ s see if we can do the very same. thing with compound rate of interest. Allow me remove all this. That ‘ s not how I. intended to remove it.
There we go. OK, so’with substance passion,. in year 1, it ‘ s the very same point, really, as straightforward
passion, and.
we saw that in the previous video.I owe P plus, and now the price. times P, which equals P times 1
plus r. Fair sufficient. Currently year 2 is where substance. and basic interest split.
In easy interest, we would. In compound passion,.
principal, we are going to pay 1 plus r times this, right? Our original principal was P. After one year, we paid 1 plus.
r times the initial principal times 1 plus r rate. To go into year 2, we” re. mosting likely to pay what we owed at the end of year 1, which is P.
times 1 plus r, and then we” re going to expand that.
We” re going to increase. The method you could think.
about it, in straightforward passion, every year we included a Pr. In straightforward interest, we.
included plus Public relations each year. If this was $50 and this is.
15%, yearly we” re adding$ 3– we ‘ re including–. what was that? 50 %.
We ‘ re adding $7.50 in rate of interest,. where P is the principal, r is
the price’. In compound passion, every. year we ‘ re multiplying the principal times 1 plus.
If we go to year 3,. Year 3 is P times 1.
plus r to the 3rd. Year t is going to be. principal times 1 plus r to the t-th power. And so let ‘ s see.
that very same example. We owe’$ 200 in this instance.
with simple interest. Allow ‘ s see what’we owe. in compound’passion.
1 plus– and what ‘ s the price? And we ‘ re loaning.
it for 20 years. So this is equal to 50 times. 1.15 to the 20th power.I recognize you can ‘ t read that,.
Allow me see what I can do regarding the 20th power
. Let me utilize my Excel and. clear every one of this. Really, I ought to simply utilize my. mouse rather than the pen device to the clear whatever.
OK, so let me just. select an arbitrary point. I
just simply to– plus 1.15. to the 20th power, and you can use any kind of calculator:.
16.37, allow” s state. So this equals 50 times 16.37. And what ‘ s 50 times that? Plus 50 times that:$ 818. You ‘ ve now recognized that if.
somebody” s giving you a financing and they claim, oh, yeah, I” ll provide. you– you need a 20-year loan? I” m mosting likely to lend. it’to you at 15 %.
It ‘ s quite vital to. clear up whether they” re mosting likely to bill you 15% interest at.
basic passion or compound rate of interest. Because with compound rate of interest,.
you” re mosting likely to finish up paying– I imply, check out this: simply to.
borrow $50, you” re mosting likely to be paying $618 greater than if.
And not just is it compounding,. They put on ‘ t also simply compound it every year and they.
wear” t even simply compound it every six months, they in fact.
compound it continuously. Therefore you need to watch the.
next several video clips on continually intensifying.
rate of interest, and then you” ll really begin to discover.
concerning the magic of e. Anyway, I” ll see you.
done in the following video clip.
Let” s claim I ‘ m. loaning P bucks. I ‘ m borrowing– let ‘ s do some numbers. It ‘ s 50 times 4, which.
15%, every year we” re adding$ 3– we ‘ re adding–. And what ‘ s 50 times that?