Question

Nominal rate=5% compounded monthly.

Number of periods=3 years

Effective rate for 3 years = 15.7625%

What is the formula used here to get 15.7625% ?

Answer 1

Nominal rate = 5%
Effective annual rate = ((1 + i/n)^n) - 1)
Where,
I = nominal rate
n = number of compounding per year
Effective annual rate =((1+5%/12)^12)-1
Effective annual rate = 5.1162%
Effective rate for 3 years = ((1+5.1162%)^3)-1
Effective rate for 3 years = 16.1473%
Using the effective rate formula nominal rate 5% and monthly compounding the 3 year annual effective rate is 16.1473%
If the compounding happen annually then the Effective rate for 3 years would be 15.7625% as per EAR formula
workings :
Effective rate for 3 years = ((1+5.0%/1)^3)-1
Effective rate for 3 years = 15.7625%