Question

You are investing a sum of money for 4 years. You earn a simple interest rate of r = 10% for the first 2 years and j₁₂ = 6% for the last 2 years. What is the equivalent effective annual rate of return, j, you earn over each of the 4 years?

• A.

  7.98%

• B.

  8.81%

• C.

  8.07%

• D.

  7.84%

Answer 1

- Simple Interest rate for first 2 years = 10%

Effective Simple Interest of 2-year = (r*t)

where, r = Simple Interest rate = 10%

t = no of years = 2

Effective Simple Interest of 2-year = (0.10*2)

Effective Simple Interest of 2-year =  0.20 or 20%

- Nominal Interest rate for last 2 years = 6% compounded monthly

Calculating its Effective 2-year Interest Rate:-

Effective 2-year Interest Rate

where, r = Nominal Interest rate = 6%

t = no of years = 2

m = no of times compounding in ayear = 12

Effective 2-year Interest Rate

Effective 2-year Interest Rate = 1.12715977621 - 1

Effective 2-year Interest Rate = 12.7160%

Now, calculating effective annual rate over 4-year period:-

Effective annual rate over 4-year period = [(1+Effective Simple Interest of 2-year)*(1+Effective 2-year Interest Rate )]^(1/n) - 1

where, n = no of years = 4

Effective annual rate over 4-year period = [(1+0.20)*(1+0.127160)]^(1/4) - 1

Effective annual rate over 4-year period = (1.352592)^(1/4) - 1

Effective annual rate over 4-year period = 1.0784 - 1

Effective annual rate over 4-year period = 7.84%

option D

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