Question

An investor earns 15% in year i,-5% in year 2, and 8% in year 3. What is the effective interest rate for the 3 year period?

Plz explain the formula for this question in depth and how it is formed?

Answer 1

Answer:

Let us assume we invest amount = 1

At the end of year 1 amount will be = 1 + 15%

At the end year 2 amount will be = (1 + 15%) * (1 - 5%)

At the end year 3 amount will be = (1 + 15%) * (1 - 5%) * (1 + 8%)

Effective interest rate for 3 year period = ((1 + 15%) * (1 - 5%) * (1 + 8%)) ^(1/3) - 1

= 5.6692% or 5.7%

Alternately:

Effective annual interest rate = (Ending Value / Beginning value)^1/n - 1

Beginning value =1

Ending value = (1 + 15%) * (1 - 5%) * (1 + 8%) = 1.1799

Effective annual interest rate = 1.1799 ^(1/3) - 1

= 5.6692% or 5.7%