Compound Interest and e (part 4)

Continuously compounding for multiple years.

Category:

Education

Tags:

• finance
• math
• compound
• interest
• continuous

[uburex97]

Have been teaching finance for ages but have no math background. Although I could glibly state that FV = Per^t I could never explain why in detail - UNTIL NOW - thanks! Still worth pointing out that although quants use exp function all the time, it never occurs in the real world. Interest is always quoted periodically.

[samlocal88]

Hey Sal, does it work the same way when you're earning interest say on a savings acount? Or do they only compound your interst once a year? And how would that formula look like (to calculate your savings in time) Thanks!

[jnnycliff]

Imagine: ? x compound x Inflation x Fractional server x interest = American Fxxked.

[KiritaWindwalker]

I dont have the button for log on my calculator. Is there a different way to do it on a normal one? Or maybe to find by hand?

[Myrslokstok]

Well is it not beqause f(x)=e^x ger f'(x)=e^x that it is called natural. It is the natural base for diferetiation.

[jchien]

I have a permanent neuron for Pe^rt in my brain now thanks to Sal.

[reik2006]

so cool realizing the connection to differential equations y(t)'=ry(t) with the solution y=Ce^rt right here ... the principal C as the initial value at time t=0 and so on ;) ... so funny how all the stuff is interconnected .. so much fun :D

[undercover9999]

@samlocal88 I haven't seen compounded interest rate (e based; t=max 12 or monthly) on loans. Regarding savings you can get monthly compounded interest (when you choose 1M deposit and renew it automatically). e based compounded interest is used only in finance calculations and some bond trades. This e based compounded interest in advanced finance calculation and it is used more in theory than in real life situations.

[Subutubiata]

He's left T out of the equation at 3.08.

[Subutubiata]

Okay. At 3.08 Sal gives the formula for calculating compound interest as: '1000 x e to the power of .75 x 3. In other words the principal multiplied by e raised to the power of the rate multiplied by the year (T).

But if you look at what he does on the spreadsheet he seems to omit the 3 (t). He's performing a compound interest calculation for period, with no time passed since the loan issue..., or what?.