The following money market account rates were available from a particular bank. Find the compound amount and the interest earned. $$ \$ 75,000 $$ at $$ 0.91 \% $$ compounded quarterly for nine years The compound amount is $$ \$ \square $$. (Do not round until the final answer. Then round to the nearest cent as needed.) The amount of interest earned is $$ \$ \square $$. (Do not round until the final answer. Then round to the nearest cent as needed.)

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To find the compound amount and the interest earned for the given money market account rates, we can use the formula for compound interest:

$$ A = P \left( 1 + \frac{r}{n} \right)^{nt} $$

where:
- $$ A $$ is the compound amount
- $$ P $$ is the principal amount (initial deposit)
- $$ r $$ is the annual interest rate
- $$ n $$ is the number of times the interest is compounded per year
- $$ t $$ is the time in years

Given:
- Principal amount $$ P = \$75,000 $$
- Annual interest rate $$ r = 0.91\% = 0.0091 $$
- Compounded quarterly, so $$ n = 4 $$
- Time $$ t = 9 $$ years

Let's calculate the compound amount and the interest earned using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$75000\left(1+\frac{0.0091}{4}\right)^{4}\times 9$$
- step1: Divide the terms:
  $$75000\left(1+\frac{91}{40000}\right)^{4}\times 9$$
- step2: Add the numbers:
  $$75000\left(\frac{40091}{40000}\right)^{4}\times 9$$
- step3: Multiply the terms:
  $$675000\left(\frac{40091}{40000}\right)^{4}$$
- step4: Simplify:
  $$675000\times \frac{40091^{4}}{40000^{4}}$$
- step5: Rewrite the expression:
  $$5000\times 135\times \frac{40091^{4}}{40000^{4}}$$
- step6: Rewrite the expression:
  $$5000\times 135\times \frac{40091^{4}}{5000^{4}\times 8^{4}}$$
- step7: Reduce the numbers:
  $$135\times \frac{40091^{4}}{5000^{3}\times 8^{4}}$$
- step8: Rewrite the expression:
  $$5\times 27\times \frac{40091^{4}}{5000^{3}\times 8^{4}}$$
- step9: Rewrite the expression:
  $$5\times 27\times \frac{40091^{4}}{625^{3}\times 8^{3}\times 8^{4}}$$
- step10: Rewrite the expression:
  $$5\times 27\times \frac{40091^{4}}{5^{12}\times 8^{3}\times 8^{4}}$$
- step11: Reduce the numbers:
  $$27\times \frac{40091^{4}}{5^{11}\times 8^{3}\times 8^{4}}$$
- step12: Multiply the fractions:
  $$\frac{27\times 40091^{4}}{8^{7}\times 5^{11}}$$
The compound amount is approximately $681,163.49.

Now, let's calculate the interest earned by subtracting the principal amount from the compound amount.
Calculate the value by following steps:
- step0: Calculate:
  $$681163.49-75000$$
- step1: Subtract the numbers:
  $$606163.49$$
The interest earned is approximately $606,163.49.

Therefore, the compound amount is $681,163.49 and the interest earned is $606,163.49.
The compound amount is \$681,163.49 and the interest earned is \$606,163.49.

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