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Imagine if you got $100 for your birthday and you are currently 17 years old, you put it in the bank and never touched the money. If the bank was paying 5% interest, can you guess how much money you would have on your 65th birthday? Explain your answer.

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Final answer:

After depositing $100 into a bank account with an annual compound interest rate of 5% at age 17, by age 65, you would have approximately $$1040.1, having used the formula A = P(1 + r/n)^(nt) to calculate compound interest over 48 years.

Step-by-step explanation:

To calculate how much money you would have on your 65th birthday after depositing $100 on your 17th birthday with an annual compound interest rate of 5%, 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.

If the interest is compounded annually (n=1), we plug in the values:

  • P = $100
  • r = 5% or 0.05
  • n = 1
  • t = 65 - 17 = 48 years

The formula becomes:
A = 100(1 + 0.05/1)^(1*48)

Calculating this
A = 100(1 + 0.05)^48
A = 100(1.05)^48
A ≈ 100(10.401)
A ≈$1040.

By your 65th birthday, you would have approximately $1040.1

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