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Answer :
Final answer:
The correct equation to calculate how much should be invested today to achieve $10,000 in 15 years with an average yearly growth factor of 1.09 is c. 10000 = x(1.09) ^ 15, based on the compound interest formula.
Explanation:
The student aims to have $10,000 after 15 years through an investment with a yearly growth factor of 1.09. The correct equation to calculate how much should be invested today can be derived from the formula for compound interest, which is Final Amount = Principal Amount x (1 + Growth Rate)^Number of Periods.
In this case, we want to find the principal amount that would amount to $10,000 after 15 years at a growth rate of 1.09 per year.
Therefore, the correct equation that should be used to find out how much one should invest today is:
c. 10000 = x(1.09) ^ 15
This equation is based on the compound interest formula: you're solving for x, the initial investment (or principal), that would grow to $10,000 over the course of 15 years with a compound interest rate of 9% annually (a growth factor of 1.09).
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