Question 2 You deposit $$ \$ 5000 $$ each year into an account earning 6\% interest compounded annually. How much will you have in the account in 25 years? Note: Round your answer to the nearest cent. Question Help: Video 1 Video 2 Message instructor Calculator

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We are dealing with an annuity where you deposit a fixed amount each year. The formula for the future value of an annuity (with deposits made at the end of each period) is given by

$$
\text{FV} = D \times \frac{(1+r)^n - 1}{r}
$$

where 
- $$ D $$ is the annual deposit,
- $$ r $$ is the annual interest rate (in decimal), and
- $$ n $$ is the number of years.

Given in the problem:
- $$ D = 5000 $$,
- $$ r = 0.06 $$, and
- $$ n = 25 $$.

Substitute these values into the formula:

$$
\text{FV} = 5000 \times \frac{(1.06)^{25} - 1}{0.06}
$$

Step 1: Compute $$(1.06)^{25}$$.

Using a calculator,

$$
(1.06)^{25} \approx 4.29187
$$

Step 2: Subtract 1:

$$
4.29187 - 1 = 3.29187
$$

Step 3: Divide by $$0.06$$:

$$
\frac{3.29187}{0.06} \approx 54.8645
$$

Step 4: Multiply by 5000:

$$
\text{FV} \approx 5000 \times 54.8645 \approx 274322.50
$$

Thus, after 25 years, the amount in the account will be approximately

$$
\boxed{\$274322.50}
$$
After 25 years, you will have approximately \$274,322.50 in the account.

Question 2 You deposit \( \$ 5000 \) each year into an account earning 6\% interest compounded annually. How much will you have in the account in 25 years? Note: Round your answer to the nearest cent. Question Help: Video 1 Video 2 Message instructor Calculator

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