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The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b).




Principal		RateCompoundedTime

\$1500		2.6\%daily3.5 years





AFind how much money there will be in the account after the given number of years. (Assume 365 days in a year.)



The amount of money in the account after 3.5 years is \$ ___ .

(Round to the nearest cent as needed.)


BFind the interest earned.



The amount of interest earned is \$ ___ .

(Round to the nearest cent as needed.)

Verified Answer :

  • The interest earned is calculated by subtracting the initial principal from the final account balance.
  • Given \(A = \$1642.90\) and \(P = \$1500\), we compute \(I = A - P\).
  • The total interest earned is \(\boxed{\$142.90}\).

Explanation

  1. Understanding the Interest Calculation

The problem asks us to calculate the total interest earned on an investment of \(\$1500\) that grows with daily compound interest at an annual rate of \(2.6\%\) over a period of \(3.5\) years. We are given that the final amount in the account after this period is \(\$1642.90\). The interest earned, denoted as \(I\), is the difference between the final account balance \(A\) and the initial principal \(P\). Thus, the formula is:
\[I = A - P\]

  1. Calculating the Interest Earned

To find the interest earned, we substitute the given values into the formula:

  • Principal \((P) = \$1500\)
  • Final Amount \((A) = \$1642.90\)

Calculating the difference:
\[I = 1642.90 - 1500\]
\[I = 142.90\]
Therefore, the total interest earned over the 3.5-year period is \(\$142.90\).

Examples

Compound interest is a fundamental concept in finance that demonstrates how money can grow over time. For example, if you save \(\$500\) in a bank account that earns \(2\%\) interest compounded monthly, your balance will increase more each month because you earn interest on your interest, not just on your initial \(\$500\). This principle is the foundation for growing wealth through savings accounts, investments, and retirement funds, showing the power of time and consistency in financial planning.

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