Xavier opened a savings account with a deposit of $12,000. The account earned simple interest. He did not make any additional de
1 answer:
The annual interest rate on the saving account of Xavier which is earned simple interest is 9%.
<h3>What is simple interest?</h3>Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.
The formula for the simple interest can be given as,
Here, (<em>I</em>) is the interest amount on the principal amount of (<em>P</em>) with the rate of (<em>r</em>) in the time period of (<em>t</em>).
Xavier opened a savings account with a deposit of $12,000. At the end of 3 years, the account balance was $12,324.
The principal amount is $12000 and the total amount is $12324. Thus, the interest earned by the Xavier is,
Total time period is 3 years and the account earned simple interest. Thus, put these values in the above formula as,
Hence, the annual interest rate on the saving account of Xavier which is earned simple interest is 9%.
Learn more about the simple interest here;
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Answer:
a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45
b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25
c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75
d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).
And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.
And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.
Step-by-step explanation:
For this case we can use the following formulas for the mean and standard deviation:
Part a
Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45
And if we calculate the mean we got:
Part b
For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:
44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25
And if we calculate the new mean and deviation we got:
Part c
The new dataset would be each value divided by 12 so we have:
3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75
And the new mean and deviation would be:
Part d
As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).
And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.
And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.