Quantitative Methods #1: Time Value Of Money Basics

In this post, I will go over some basics that you must know before attempting your CFA exam. I do not want to start with Ethics for reasons that I will explain later on so let’s get into Quantitative Methods. It’s a tricky section, that does not count for much. In my opinion, it’s fairly easy to get a “decent score” in quants because the basics are fairly easy to understand and get a grip on. The real challenge is getting very high scores here. Let’s start off with the easiest but probably most important part of the section:

Time Value of Money Basics

The concept is simple enough. If you put a sum of money into your bank account for 1 year, at the end of that year you will have a bit more money then you had. How much more? It depends on 3 simple things.

-How much you have initially? (PV)
-What rate you are receiving? (I)
-How much time the money is invested? (T)

The formula that you have is:

FV (future value) = PV*(1+I)^T

You need to understand the formula because, it’s critical but you don’t need to know it by heart. The formula can be moved in a different ways and you can find any of the 4 terms as long as you have the other 3.

For example…how much money would I need to invest now at 5% during 2 years in order to get $25,000?

Here is what you have:

PV: ??
FV= $25,000
I= 5%
T=2

So:

FV (future value) = PV*(1+I)^T
$25,000 = x * (1+0,05)^2
$25,000= 1,1025x
x = $22,675.74

So you would need to have $22,675.74. This concept like many others is presented in quant but required in many other parts of the exam.

Annuities And Perpetuities

What is an annuity? It is a series of cash flows that will take place over time. By default, the payment would be made at the end of each period. For example, if you and the New York Yankees make a deal to name their stadium “Citi Field,” they could receive an annuity of $5 million each year during 25 years for example.

A perpetuity is similar but has no end. So an example would be giving $500 each year with no end date.  How do you calculate it? Simple:

Value of a perpetuity=  Payment / Discount rate

So a payment of $500 discounted at a rate of 5% would be worth

PV = $500/0.05
PV = $10,000

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