Silly mistake in Harvard Business school's Course ;) - Mathematics

Hello Internet,

Last day i was going through the Online course for my semester. The course is quiet informative and simple explains all the basic concepts in a very precise and interactive way. You can give it a try its worth it.

But there's an error here as well .It's an easy one .But yes may bother someone, so save your time
Formula for Annuity and calculating the  bond value !

C(1r−1r(1+r)N)+F(1+r)N

The answer will change from 3.8554 to 3855432894.295317473644036444788 . That's a big change :D. Funny fact is they always end up with correct answers like we do :D ! Let me know if you guys figure out some other mistake as well.

I've dropped an email will be corrected soon. 

That's all Folks
Nitin Arya

IBAN error Deutsche Bank

Deutsche Bank is sending wrong IBAN in new block account letters.

IBAN structure

So today i was about to transfer my funds in my account and the payment gateway kept denying the IBAN number given by the Deutsche bank .

IBAN is of 22 Digits and here  in the  attached letter u'l see they have given a 21 digit IBAN. I am wondering how can they commit a mistake like that when they are opening more than thousands of block account daily. Maybe a lot of people have been facing same problem regarding their IBAN.

Here's Proof of concept I hope they fix it soon.
Full size Image :- https://twitter.com/nitin0arya/status/365517556691386371/photo/1

Deutsche Bank

Simplifying Annuity

The present value of a constant cash flow, C, for t periods is:

Define the discount factor:

Substituting a into the formula, we get

To simplify the present value formula, we need to simplify the expression in the brackets:

To simplify this formula, we first add at+1,at+2, and so on, and then subtract all the terms we added:

We can rewrite this as:

Note that the infinite number of terms in each of the brackets is the same. Define:

+

Now, observe that V = 1 + aV, which means that

Therefore, the expression

Now, replace a with the discount factor 1/(1 + r) and simplify to get:

We can now simplify the present value formula as follows:

Replacing the expression in square brackets with what we derived, we get:

Simplified Annuity

which is the annuity formula.

Given the interest rate, r, this formula can be used to compute the present value of the future cash flows. Given the present value, it can be used to compute the interest rate or yield. Finally, given the present value and the interest rate, it can be used to determine the cash flow.

You can use the formula in different ways as you go through Bond Tutor. The topic Time Value of Money in this chapter lets you calculate the present value of each cash flow for an annuity and also lets you see the annuity value through time. In The Term Structure of Interest Rates topic, you can see how the present value is affected by the interest rate and also calculate the interest rate given the present value.

Courtsey & Source http://www.bondtutor.com/btchp1/topic7/topic7.htm

Nitin Arya

NPV and IRR explained with example.

Hello everyone,

One of the main confusion that pops is regarding the conceptual difference b/w the IRR(Internal Rate of Return ) and NPV(Net Present Value).

Now we can easily understand the underlying formulas and calculations but there is an idea that has to be understood and the best to to understand is by picking up an suitable example.

I would suggest this Wiki article for a warm up.

http://en.wikipedia.org/wiki/Internal_rate_of_return

http://en.wikipedia.org/wiki/Net_present_value 

Example:- We need two investments for which the net NPV should be 50.
Cost of Capital = .2 or 20%

Investment one:       -100                 180

Investment two:       -100000           120060

NPV one = -100 + 180(1 + .2) = 50
NPV two = -100000 + 120060(1 + .2) = 50

You cannot judge an investment based on NVP as both are same but consider the amount of money in investment two but this is just an simple case when the investments are complex its hard to judge so . So that's why we need IRR but IRR is also not the ultimate solution.

Now lets calculate IRR for the same . We need a value r' for which the NVP must be Zero.

IRR one :-  -100  + 180/(1 + r') = 0
                  Simplify we get r' = 0.80 

IRR two :-    -100000 + 120060(1+r'')= 0
                     here r'' = .2006

r < r'  Investment  accepted

  r > r ' Investment rejected

In our case r  = .20 and r'= .80 and r''(Second investment) = .20

So clearly investment one is favorable as compared to investment two although up to fourth decimal place it is also higher or up to second decimal place almost equal but as you read wiki page carefully you see these methods are for mutually exclusive investment selection and thus investment one gives us higher return and thus should be chosen.

Nitin Arya