You can Get a Similar Question 98 more times Find the $$ \$ 7,800 $$ is deposited at $$ 4 \% $$ interest compounded quarterly (every 3 months) and the money is left for 7 years. The final amount is $$ \$ $$ $$ \square $$ . Round answer to 2 decimal places Submit Question Question 6 5/5 pts $$ 2 \leftrightarrows 99 $$ Details

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To find the final amount after 7 years with a deposit of $7,800 at a 4% interest compounded quarterly, we can use the formula for compound interest:

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

Where:
- $$ A $$ is the final 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:
- $$ P = \$7,800 $$
- $$ r = 4\% = 0.04 $$
- $$ n = 4 $$ (compounded quarterly)
- $$ t = 7 $$ years

Substitute the values into the formula:

$$ A = 7800 \left( 1 + \frac{0.04}{4} \right)^{4 \times 7} $$

Now, we can calculate the final amount.
Calculate the value by following steps:
- step0: Calculate:
  $$7800\left(1+\frac{0.04}{4}\right)^{4\times 7}$$
- step1: Divide the terms:
  $$7800\left(1+\frac{1}{100}\right)^{4\times 7}$$
- step2: Add the numbers:
  $$7800\left(\frac{101}{100}\right)^{4\times 7}$$
- step3: Multiply the numbers:
  $$7800\left(\frac{101}{100}\right)^{28}$$
- step4: Simplify:
  $$7800\times \frac{101^{28}}{100^{28}}$$
- step5: Rewrite the expression:
  $$100\times 78\times \frac{101^{28}}{100^{28}}$$
- step6: Reduce the numbers:
  $$78\times \frac{101^{28}}{100^{27}}$$
- step7: Rewrite the expression:
  $$2\times 39\times \frac{101^{28}}{100^{27}}$$
- step8: Rewrite the expression:
  $$2\times 39\times \frac{101^{28}}{4^{27}\times 25^{27}}$$
- step9: Rewrite the expression:
  $$2\times 39\times \frac{101^{28}}{2^{54}\times 25^{27}}$$
- step10: Reduce the numbers:
  $$39\times \frac{101^{28}}{2^{53}\times 25^{27}}$$
- step11: Multiply the fractions:
  $$\frac{39\times 101^{28}}{2^{53}\times 25^{27}}$$
The final amount after 7 years with a deposit of $7,800 at a 4% interest compounded quarterly is approximately $10,306.07.

Therefore, the final amount is $10,306.07.
The final amount after 7 years is $10,306.07.

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