Final answer:
To determine how long it will take for a $250,000 investment to grow to $1,000,000 with an 8% annual return, the compound interest formula is used. Assuming the interest is compounded annually, it will take approximately 18 years for the investment to reach $1,000,000 and make your mother a millionaire.
Step-by-step explanation:
You are asking about how long it will take for an initial investment to grow to a certain amount through the power of compound interest. The process of calculating this is a key principle in finance and investing.
Let's use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
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- A is the amount of money accumulated after n years, including interest.
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- P is the principal amount (the initial amount of money).
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- r is the annual interest rate (decimal).
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- n is the number of times that interest is compounded per year.
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- t is the time the money is invested for in years.
Your mother's case involves an initial investment of $250,000 that she wants to grow to $1,000,000 with an 8% annual return. We are solving for 't' when A=$1,000,000, P=$250,000, r=0.08, and we will assume that interest is compounded once per year (n=1).
The equation will look like: $1,000,000 = $250,000(1 + 0.08/1)^(1*t).
Solving for 't', you'll find that it takes approximately 18 years for your mother to become a millionaire with this investment strategy.