Question

will $6000 amount to in 10 years if invested at a 6% effective annual rate for the first 5 years and than at a rate of 3% compounded semi annually?

Answer 1

What will $ 6000 amount to ?

6000 is the principle and also single deposit. For future value we use the relation as ..........

Future value = Present value * (1+r)ⁿ  

This equation can be written as ....... Principle * ( 1 + r1 )n1 * ( 1 + r2)n - n1 ......... when we have different interest rates between present and future values.

r1 = 0.06 ( annual rate )

n = 10 years but n1 = 5 years ......... i.e first 5 years with annual compounding

n - n1 ......... = 10 - 5 = 5 years, but we take it as 5 years * 2 = 10 semi annual periods

= 6000 * (1.06)⁵ * (1.03)¹⁰= 10790.78 .............. final answer.

NOTE

3% rate is not mentioned as annual rate. Hence it is directly a semi annual rate.

Comment for any further clarity on this concept ......... Hope helped you.