The problem asks us to find the future value of an annuity. We are given that the payment is $1800 per year, the interest rate is 5% per year, the term is 15 years, and the payments are made at the end of each year. We need to round our final answer to the nearest cent.

1. Problem Description

The problem asks us to find the future value of an annuity. We are given that the payment is $1800 per year, the interest rate is 5% per year, the term is 15 years, and the payments are made at the end of each year. We need to round our final answer to the nearest cent.

2. Solution Steps

We will use the formula for the future value of an ordinary annuity:

$FV = P * \frac{(1 + r)^n - 1}{r}$

Where:

$FV$ is the future value of the annuity

$P$ is the periodic payment

$r$ is the interest rate per period

$n$ is the number of periods

In this case, $P = 1800$, $r = 0.05$, and $n = 15$.

Plug these values into the formula:

$FV = 1800 * \frac{(1 + 0.05)^{15} - 1}{0.05}$

$FV = 1800 * \frac{(1.05)^{15} - 1}{0.05}$

Calculate $(1.05)^{15}$:

$(1.05)^{15} \approx 2.0789281794$

Substitute this value back into the formula:

$FV = 1800 * \frac{2.0789281794 - 1}{0.05}$

$FV = 1800 * \frac{1.0789281794}{0.05}$

$FV = 1800 * 21.578563588$

$FV = 38841.4144584$

Round the answer to the nearest cent:

$FV \approx 38841.41$

3. Final Answer

$38841.41