Question 1208832: Investing $8,000 for 6 years.
Option #1
7% compounded monthly
Option #2
6.85% compounded continuously
Which is the better investment? Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Option 1
A = P*(1+r/n)^(n*t)
A = 8000*(1+0.07/12)^(12*6)
A = 12160.84 approximately when rounding to the nearest penny
Option 2
A = P*e^(r*t) where e = 2.718 roughly
A = 8000*e^(0.0685*6)
A = 12066.60 approximately when rounding to the nearest penny
You earn slightly more with option 1.
The difference is 12160.84 - 12066.60 = 94.24 extra dollars.
In order for to determine which investment is better in this problem,
there is no need to calculate the final future value after 6 years.
It is enough to count the effective growth factor in one year.
From one side hand, we have the effective yearly growth factor of
= 1.072290081... (for 7% compounded monthly)
From the other side, we have the effective yearly growth factor
= = 1.070900576... (for 6.85% compounded continuously)
Where yearly effective yearly growth factor is greater, there the investment is better.
ANSWER. Option 1 is better.
(