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Question 18 [5 points] How many years would it take for 8,000 to grow to 30,000 with an annual rate of change of 9.901149% ? For full marks your answer(s) should be rounded to the nearest whole year. Number of years =0

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Question 18 [5 points] How many years would it take for 8,000 to grow to 30,000 with an annual rate of change of 9.901149% ? For full marks your answer(s) should be rounded to the nearest whole year. Number of years =0

Question 18 [5 points] How many years would it take for 8,000 to grow to 30,000 with an annual rate of change of 9.901149% ? For full marks your answer(s) should be rounded to the nearest whole year. Number of years =0

Solution

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FelicityProfessional · Tutor for 6 years

Answer

<p> 44</p>

Explain

<p> This is a question of compound interest. The formula for compound interest is A=P(1 + r/n)^(nt), where A is the future value of the investment/loan, including interest, P is the principal investment amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed for.<br /><br />In the question, you are asked to calculate the number of years it would take for an initial investment of $8000 to grow to$30000 with an annual interest rate of 9.901149% (or 0.09901149 in decimal form). This gives you the equation 30000 = 8000*(1 + 0.09901149)^t.<br />Solving for t by using the logarithm method gets you approximately 44 years.</p
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