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mel-nik [20]
3 years ago
10

You deposit $75 in a savings account that earns 5% annual interest compounded yearly. Find the balance in the account after the

given amounts of time. 1 year 2 years 5 years 20 years
Mathematics
1 answer:
Nana76 [90]3 years ago
7 0
Hi there
The formula is
A=p (1+r)^t
A future value
P present value 75
R interest rate 0.05
T time

After 1 year the balance is
A=75×(1+0.05)
A=78.75

After 2 years
A=75×(1+0.05)^(2)
A=82.69

After 5 years
A=75×(1+0.05)^(5)
A=95.72

After 20 years
A=75×(1+0.05)^(20)
A=198.99 round
A=199

Hope it helps
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Answer:

a) Figure attached

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So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

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After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=10 \sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274  

r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989  

So then the correlation coefficient would be r =0.989

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