A large brine tank containing a solution of salt and water is being diluted with fresh water. The relationship between the elaps
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Answer:
Part A)
About $3767.34.
Part B)
About $3692.47.
Step-by-step explanation:
Part A)
Recall that compound interest is given by the formula:
Where <em>A</em> is the final amount, <em>P</em> is the initial amount, <em>r</em> is the interest rate, <em>n</em> is the number of times compounded per year, and <em>t</em> is the number of years.
To obtain $4000 after two years, let <em>A</em> = 4000 and<em> t</em> = 2.
Because the account pays 3% interest compounded monthly, <em>r</em> = 0.03 and <em>n</em> = 12.
Substitute and solve for <em>P: </em>
<em />
In concluion, about $3767.34 should be deposited.
Part B)
Recall the formula for continuous compound:
Where <em>e</em> is Euler's number.
Hence, let <em>A</em> = 4000, <em>r</em> = 0.04 and <em>t</em> = 2. Substitute and solve for <em>P: </em>
<em />
In conclusion, about $3692.47 should be deposited.
From the problem we know that Hanna saves one-half of her paycheck each week, so she saves 
. Also, we know that her parents put $50 in her savings account each week, so the total amount she and her parents put in her saving's account is 
.
Since we know that Hanna currently has <span>$1,280 in her saving's account and each week she and her parents deposit $130 to the account, with </span>
representing the number of weeks, we can model the situation as follows:
Since we know that Hanna currently has <span>$1,280 in her saving's account and each week she and her parents deposit $130 to the account, with </span>