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Suppose you deposit $3,250 to a bank, which offers an annual interest rate of 4.75%, compounded daily, how much do you have after 4 years? (Assume there are only 365 days in a year)

User Melanee
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Final answer:

To calculate the future value of $3,250 with daily compound interest at an annual rate of 4.75% over 4 years, the compound interest formula is used. The values are substituted into the formula A = P(1 + r/n)^(nt) to compute the final amount in the account after the given period.

Step-by-step explanation:

The question involves calculating the future value of an investment with daily compound interest. To determine the amount in the account after 4 years, 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 or borrowed for, in years.

In this case, P is $3,250, r is 4.75% or 0.0475 in decimal form, n is 365 (since the interest is compounded daily), and t is 4 years. Substituting these values into the formula, we get:

A = 3250(1 + 0.0475/365)^(365*4)

Using a calculator, we compute the value of A to reach the final amount.

User Callum Watkins
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