Final answer:
To have $10,000 in ten years in an account with a 10% interest rate compounded annually, you must deposit approximately $3855.43 today.
Step-by-step explanation:
To determine how much money you need to deposit in a bank account with a 10% interest rate compounded annually to have $10,000 in ten years, you can use the formula for compound interest:
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.
Since the interest is compounded annually, n is 1. We are given A = $10,000, r = 10%, or 0.10, and t = 10 years. Rearranging the formula to solve for P gives us:
P = A / (1 + r)t
Now replace A with $10,000, r with 0.10, and t with 10:
P = $10,000 / (1 + 0.10)10 = $10,000 / (1.10)10
Using a calculator:
P = $10,000 / 2.59374... = $3855.43 (approximately)
Hence, you would need to deposit approximately $3855.43 into the account today to have $10,000 in ten years, considering the given interest rate and compounding frequency.