5) An Investor has the opportunity to make an investment that will provide an ef

Question

5) An Investor has the opportunity to make an investment that will provide an effective annual yield of 10 percent. She is considering two other investments of equal risk that will provide compound interest monthly and quarterly respectively. What must the equivalent nominal annual rate ( ENAR) be for each of these two investments to ensure that an equivalent annual yield of 10 percent is earned? A. Find the ENAR for 10 % EAY given monthly compounding. B. Find the ENAR fo 10 % EAY given quarterly compounding

Explanation / Answer

A)

Nominal interest rate for a period with effective interest rates in it's sub-periods can be calculated as

i = (1 + ie)n - 1   

where

i = nominal interest rate for the period

ie = effective interest rate for the sub-period

n = number of sub-periods

Effective Rate per Period (I)

10%

Compounding per Period (m) 12

Number of Periods (t) 1 year

B) similarly for quarterly

Effective Rate per Period (I)

10%

Compounding per Period (m) 3

Number of Periods (t) 1 year

ENAR (Nominal Rate per Period:)
r = 9.684%

Rate per Compounding Intereval:
p = 3.22801%

Effective Rate per Period (I)

10%

Compounding per Period (m) 12

Number of Periods (t) 1 year

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