Question

11. 8 What compound interest rate, j, is equivalent 6% the first year, followed by a simple discount rate of 8% for the next 2 years? 3-year period to a simple interest rate of over a

Please show work

Answer 1

Simple interest rate for year 1 = 6%

As simple discount rate for next 2 years is 8%, therefore

Simple interest or discount rate for year 2 = Simple interest or discount rate for year 3 = 8%

(1 + Effective annual interest rate over 3 years)³ = (1 + Simple interest rate for year 1)(1 + Simple interest rate for year 2)(Simple interest rate for year 3)

(1 + Effective annual interest rate over 3 years)³ = (1 + 6%)(1 + 8%)(1 + 8%) = 1.06 x 1.08 x 1.08 = 1.236384

Effective annual interest rate over 3 years = (1.236384)^1/3 - 1 = 1.07329175 - 1 = 0.07329175 = 7.329175%

Quarterly rate = i₄ = (1 + Effective annual interest rate over 3 years)^1/4 - 1

= (1 + 7.329175%)^1/4 - 1 = (1.07329175)^1/4 - 1 = 1.0178398 - 1 = 0.0178398 = 1.78398%

J₄ = Nominal rate = 4 x i₄ = 4 x 1.78398% = 7.1359% = 7.14% (rounded to two decimal places)

Hence compounded growth rate j₄ = 7.14%