Answer:
r = 0.046212737
Step-by-step explanation:
A = 14,400 (what your investment originally is)
P = 7,200 (what you want your investment to be)
n = 365 (interest is compounded daily)
t = 15 (15 years)
Plug all of these numbers into the equation, then solve for r
14,400 = 7,200(1 + r/365)^365 · 15
Divide 7,200 on both sides --> 2 = (1 + r/365)^365 · 15
365 · 15 = 5475 --> 2 = (1 + r/365)^5475
5475√(2) = 1 + r/365 (root 5475 both sides to cancel out the exponent)
(5475√(2)) - 1 = r/365 (subtract one from both sides)
((5475√(2)) - 1) · 365 = r (multiply both sides by 365 to isolate r)
Type the left side into the calculator to get r --> 0.046212737.
Hope this helps!
By inspection, it's clear that the sequence must converge to
because
when
is arbitrarily large.
Now, for the limit as
to be equal to
is to say that for any
, there exists some
such that whenever
, it follows that
From this inequality, we get
As we're considering
, we can omit the first inequality.
We can then see that choosing
will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that
.
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It would be 10 because 6.4 is greater than 5. Correct me if i’m wrong
