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If you deposit $348.00 into an account paying 19.79% annual interest compounded quarterly, how many years until there is $24,420.00 in the account?

User Theotherdy
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1 Answer

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Final answer:

To calculate the number of years it will take for $348.00 to grow to $24,420.00 at an annual interest rate of 19.79% compounded quarterly, the compound interest formula is used, solving for the time variable t.

Step-by-step explanation:

To determine how many years it will take for an initial deposit of $348.00 to grow to $24,420.00 in an account with an annual interest rate of 19.79% compounded quarterly, we use the compound interest formula:

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.

In this case, the principal P is $348.00, the annual interest rate r is 0.1979, the interest is compounded quarterly so n is 4, and we want the final amount A to be $24,420.00. We need to solve for t.

Transforming the compound interest formula to solve for t gives us:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values:

t = (log(24420/348)) / (4 * log(1 + 0.1979/4))

By calculating this expression, we can find out how many years it will take for the initial deposit to grow to the desired amount.

User Sudhakar Chavali
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8.2k points
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