7.3: annuities\nscore: 1/19 answered: 1/11\nquestion 2\nyou deposit $2000 at the end of each year into an…

Explanation:

Step1: Identify the annuity - formula

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Determine the values of $A$, $r$, and $n$

Given that $A=$2000$, $r = 0.02$ (since $2%=0.02$), and $n = 15$.

Step3: Substitute the values into the formula

$F=2000\times\frac{(1 + 0.02)^{15}-1}{0.02}$. First, calculate $(1 + 0.02)^{15}$. Using the formula $a^{b}$, we have $(1.02)^{15}\approx1.345868$. Then $(1.02)^{15}-1\approx1.345868 - 1=0.345868$. And $\frac{(1.02)^{15}-1}{0.02}=\frac{0.345868}{0.02}=17.2934$. Finally, $F = 2000\times17.2934=$34586.8$.

Answer:

$34586.8$