Mark deposited $$ \$ 500 $$ at the END of each year for 18 years in a savings account. If the account paid $$ 5 \% $$ interest, compounded annually, use Table $$ 12-1 $$ to find the future value of his account. Select one: a. $$ \$ 12,822.71 $$ b. $$ \$ 12,920.19 $$ c. $$ \$ 14,066.19 $$ d. $$ \$ 15,452.83 $$

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UpStudy AI · Accepted Answer

**Step 1. Define the Variables**

Let  
- $$ P = \$500 $$ (annual deposit)  
- $$ r = 5\% = 0.05 $$ (annual interest rate)  
- $$ n = 18 $$ (number of deposits)

Since deposits are made at the end of each year, this is an ordinary annuity.

**Step 2. Recall the Formula for the Future Value of an Ordinary Annuity**

The future value $$ FV $$ is given by:  
$$
FV = P \times \frac{(1+r)^n - 1}{r}
$$

**Step 3. Substitute the Values into the Formula**

Substitute $$ P = 500 $$, $$ r = 0.05 $$, and $$ n = 18 $$ into the formula:
$$
FV = 500 \times \frac{(1+0.05)^{18} - 1}{0.05}
$$

**Step 4. Calculate $$ (1+0.05)^{18} $$**

$$
(1.05)^{18} \approx 2.40662
$$

**Step 5. Compute the Future Value**

First compute the numerator:
$$
(1.05)^{18} - 1 \approx 2.40662 - 1 = 1.40662
$$
Now divide by $$ r $$:
$$
\frac{1.40662}{0.05} \approx 28.1324
$$
Multiply by $$ P = 500 $$:
$$
FV \approx 500 \times 28.1324 = 14,\!066.2
$$

**Step 6. Match with the Answer Choices**

The computed future value is approximately $$ \$14,\!066.19 $$, which corresponds to option **(c)**.
The future value of Mark's account is approximately \$14,066.19, so the correct answer is **(c) \$14,066.19**.

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