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6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent?

Question

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent?

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Solution

To solve this problem, we will use the formula for compound interest, which is A = P(1 + r/n)^(nt).

Here's what each symbol stands for:

  • 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 (in decimal form, so 8.25% becomes 0.0825).
  • n is the number of times that interest is compounded per year.
  • t is the number of years the money is invested for.

In this case, P = $6700, r = 8.25% or 0.0825 (in decimal form), n = 1 (since it's annual interest), and t = 28 years.

Substituting these values into the formula, we get:

A = 6700(1 + 0.0825/1)^(1*28)

Solving this equation will give us the total amount in the account after 28 years.

A = 6700(1 + 0.0825)^28 A = 6700(1.0825)^28 A = 6700 * 14.785 A = $99,059.50

So, after 28 years, there will be approximately $99,059.50 in the account, to the nearest cent.

This problem has been solved

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