(1)) Edgar has $$ \$ 7,000 $$ in an account that earns $$ 15 \% $$ interest compounded annually. (1) To the nearest cent, how much interest will he earn in 3 years? (1)) Use the formula $$ B=p(1+r)^{t} $$, where $$ B $$ is the balance (final amount), $$ p $$ is the principal (starting amount), $$ r $$ is the interest rate expressed as a decimal, and $$ t $$ is the time in years.

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To find the interest earned by Edgar in 3 years, we can use the formula for compound interest:

$$ B = p(1 + r)^t $$

where:
- $$ B $$ is the balance (final amount)
- $$ p $$ is the principal (starting amount)
- $$ r $$ is the interest rate expressed as a decimal
- $$ t $$ is the time in years

Given:
- Principal ($$ p $$) = $7,000
- Interest rate ($$ r $$) = 15% = 0.15 (as a decimal)
- Time ($$ t $$) = 3 years

Substitute the given values into the formula:

$$ B = 7000(1 + 0.15)^3 $$

Now, we can calculate the balance after 3 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$7000\left(1+0.15\right)^{3}$$
- step1: Add the numbers:
  $$7000\times 1.15^{3}$$
- step2: Convert the expressions:
  $$7000\left(\frac{23}{20}\right)^{3}$$
- step3: Evaluate the power:
  $$7000\times \frac{12167}{8000}$$
- step4: Multiply:
  $$\frac{85169}{8}$$
The balance after 3 years is $10,646.125.

To find the interest earned, we subtract the principal from the balance:

Interest = Balance - Principal
Interest = $10,646.125 - $7,000
Interest = $3,646.125

Therefore, Edgar will earn $3,646.125 in interest in 3 years.
Edgar will earn $3,646.125 in interest in 3 years.

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