Advance Algebra Logarithm Task
1 answer:
9514 1404 393
Answer:
3.65% monthly
Step-by-step explanation:
The same amount is invested for the same period in all accounts, so we only need to determine the effective annual rate in order to compare the accounts.
For compounding annual rate r n times per year, the effective annual rate is ...
(1 +r/n)^n -1
For the same rate r, larger values of n cause effective rate to be higher. As a consequence, we know that 3.65% compounded quarterly will not have as great a yield as 3.65% compounded monthly. The effective rate for the monthly compounding is ...
(1 +0.0365/12)^12 -1 = 3.712%
The effective rate for continuous compounding is ...
e^r -1
For a continuously compounded rate of 3.6%, the effective annual rate is ...
e^0.036 -1 = 3.666%
This tells us the best yield is in the account bearing 3.65% compounded monthly.
_____
If i is the effective annual rate of interest as computed by the methods above, then the 10-year account balance will be ...
10000×(1 +i)^10
This is the formula used in the spreadsheet to calculate the balances shown.
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Step-by-step explanation:
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Answer:
The equation of circle is +
= 18
Step-by-step explanation:
Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)
We know that the equation of circle is
+
=
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
To find (h,k): the center is midpoint of diameter
Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by
( ,
)
( ,
)
(1,2)
Hence (h,k) is (1,2)
Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get
+
=
= 18
Now substituting values of (h,k) and in equation of circle, we get
+
= 18
Hence the equation of circle is +
= 18