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What is the effective interest rate per 6 months at an interest rate of 10

User Pugmarx
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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:


  • A is the amount of money accumulated after n years, including interest.

  • P is the principal amount (the initial amount of money).

  • r is the annual interest rate (decimal).

  • n is the number of times that interest is compounded per year.

  • 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.

User Matthias Guenther
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