HOW TO - Finding Rate of Return

Problem - Find what interest was earned on an annuity in which you gave $6000 3 years back and now has $6957?

Solution

FV = 6957
PV = 6000


METHOD 1 = NTH ROOT MANNER
(1+R)pow 3 = (6957/6000)
1+R = Cube Root of (6957/6000)
1+R = 1.05
So Rate of return was 5%



METHOD 2 = LOGARITHM MANNER
(1+R)pow 3 = (6957/6000)
Take log on both sides

3 Log (1+R) = Log (6957/6000)

Log (1+R) = 0.0214

In general if we have to find the log of a number what are we finding?
We are finding an exponent to which we will raise the base (in this case 10) to get that number.

e.g Log (100) = Exponent we will raise 10 to get 100 which is 2

In the above case we already have the exponent to which we will raise 10 to get (1+R)

So that means (1+R) = 10 pow (0.0214)

1+R = 1.05
R = 5% in this case also

Reference

http://support.microsoft.com/kb/214116


=LOG(n,b) Log base b of n =LOG(8,2) 3

=(b)^(x) Inverse log of the =2^3 8
number x, base b

=LOG10(n) Log base 10 of n =LOG10(100) 2

=10^(x) Inverse log of the =10^2 100
number x, base 10

=LN(n) Natural log of n =LN(100) 4.6051702

=EXP(x) Inverse natural =EXP(4.6051702) 100
log of the number x