Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 3% for the first year, an effective rate of discount of 6% for the second year, an effective rate of discount of 9% for the third year, and an effective rate of interest of 5% for the fourth, fifth and sixth years?
A. 6.3% B. 6.4% C. 6.5% D. 6.6% E. 6.7%
So I thought we were supposed to apply this formula:
$FV=PV(1+i)^t = PV \cdot v^{-t}=PV(1-d)^{-t}$
d = rate of discount
i=effective rate of interest
v= present value factor
So my approach was this:
$(1-0.03)^{-1}(1-0.06)^{-2}(1-0.09)^{-3}(1.05)^4(1.05)^5(1.05)^6=(1+6i)$
solving for i you get 37% which is obviously wrong. Can someone please explain the proper approach? Thanks in advance.
The effective rate of (simple) interest would be: $(1 - 0.03)^{-1}(1 - 0.06)^{-1}(1 - 0.09)^{-1}(1 + 0.05)^3 = (1 + 6i) \implies i \approx 6.6\%$