Compounding formulas:

CFA Level I
#1

I am struggling to understand the difference between below two methods.

Let

N= 5

r= 6.5% compounding monthly

Pv= 100

Fv= ?

First Method:

FV= PV( 1+r)^N

FV= 100( 1+.065/12)^60

FV= 138.38

2nd Method:

FV= PV (1+r) ^N

FV= 100(1.065)^60/12

FV= 137

I am facing problem in 2nd method, i am unable to understand the logic behind this method. Kindly clarify the difference b/w these two methods and when to use the 2nd method???

#2

(1+0.065/12)^n : interest compounding 12 times per year

(1+0.065)^n: interest compounding 1 time per year

#3

Thanks for your reply.

I just want to confirm that whenever we are dealing with compounding, do we have to use the first formula?

And also please help me to understand when to use the second formula???

#4

in the first you aer compounding 6.5% per annum per month for 60 months

2nd one 6.5% per annum for 60/12=5 years

difference 138.38-137 is the effect of the extra compounding.

#5

The big concept here is that the interest rate must be consonant with the period. An effective annual rate is nothing more than the actual rate of interest or growth over a year’s time. If you assume monthly compounding, you can solve the problem as one of two ways:

  1. FV=PV x (1+0.065/12)^60 - in this case, you are treating a month as a period (and using the monthly rate of 0.065/12 as the interest rate)
  2. Alternately, you could first calculate the EAR of 6.5% with monthly compounding (it’s approximately 6.7%) and then solve the problem as FV = PV x (1.067)^5 - in this case you are using a year as a period and and the interest rate (i.e. the amount the pv grows by each year) per year.

However, if it’s annually compounded, the FV is based on number of YEARS and the 6.5% interest PER YEAR.