Jim Dandy invests a sum of money today.He earns the following interest rates over the next 5-years:
J₂ = 10% for the first 2-years
J₄ = 8% for the next 2-years
J₁₂ = 6% for the last year
What annual effective rate of return,j₁,did Jim earn over the 5-year period?

Question

Quizplus · Accepted Answer

To calculate the annual effective rate of return, we need to use the following formula:

(1 + i)^n = (1 + r1)(1 + r2)...(1 + rn)

Where i is the annual effective rate of return, n is the number of compounding periods (in this case, 5), and r1, r2, etc. are the individual interest rates for each period.

Plugging in the given interest rates, we get:

(1 + i)^5 = (1 + 0.1)^2(1 + 0.08)^2(1 + 0.06)

Simplifying:

(1 + i)^5 = 1.4644

Taking the fifth root of both sides:

1 + i = 1.085

i = 0.085 or 8.5%

Therefore, the answer is C) 8.5% or more, but less than 9%.

Jim Dandy Invests a Sum of Money Today