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9. A bank pays interest of 11% on $6000 in a deposit account

After how many years will the money have trebled?​

User MyTD
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Final answer:

To determine the number of years required for an initial deposit to triple with an 11% annual interest rate, one can use the compound interest formula and solve for time using logarithms.

Step-by-step explanation:

The question involves determining the number of years needed for an initial deposit to triple in value with an annual interest rate of 11%. To solve this problem, we can apply the formula for compound interest, which is 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 in years.

Since the money needs to treble, we can set A to 3P. The interest is not compounded more frequently than annually in this case, so n will be 1. Therefore, the equation simplifies to:

3P = P(1 + r)^t

We can cancel P from both sides and solve for t:

3 = (1 + 0.11)^t

To find t, we take the natural logarithm of both sides:

ln(3) = ln((1 + 0.11)^t)

ln(3) = t * ln(1.11)

t = ln(3) / ln(1.11)

By calculating the logarithms, we can find the number of years t required for the money to treble.

User Emel
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