Answer:
Step-by-step explanation:
No, they are not always the same - the only time that they will be the same is after the first year:
$4000*1.05 + $4000*1.07 = $8480 = $8000*1.06
From there on, they will diverge. For example after the second year:
$4000*1.05^2 + $4000*1.07^2 = $8989.6
$8000*1.06^2 = $8988.8
After the third year:
$4000*1.05^3 + $4000*1.07^3 = $9530.672
$8000*1.06^3 = $9528.128
After the nth year:
The first option gives $4000*(1.05^n + 1.07^n)
The second option gives $8000*(1.06^n)
= $4000*(2)*(1.06^n)
= $4000*(1.06^n + 1.06^n)
Because 1.07^n - 1.06^n > 1.06^n - 1.05^n for n>1, the first option will be a better investment.
