a. use the appropriate formula to find the va...
a. use the appropriate formula to find the value of the annuity. b. find the interest. periodic deposit $7000 at the end of each year rate 6.5% compounded annually time 25 years click the icon to view some finance formulas. a. the value of the annuity is $ (do not round until the final answer. then round to the nearest dollar as needed.)
Answer
# Explanation:
## Step1: Identify the formula for future - value of an ordinary annuity
The formula for the future - value of an ordinary annuity is $F = P\times\frac{(1 + r)^{n}-1}{r}$, where $P$ is the periodic payment, $r$ is the interest rate per period, and $n$ is the number of periods.
Here, $P=\$7000$, $r = 0.065$ (since $6.5\%=0.065$), and $n = 25$.
## Step2: Substitute the values into the formula
$F=7000\times\frac{(1 + 0.065)^{25}-1}{0.065}$.
First, calculate $(1 + 0.065)^{25}$.
$(1 + 0.065)^{25}=1.065^{25}\approx4.82759$.
Then, $(1.065)^{25}-1\approx4.82759 - 1=3.82759$.
$\frac{(1.065)^{25}-1}{0.065}=\frac{3.82759}{0.065}\approx58.886$.
$F = 7000\times58.886=\$412202$.
## Step3: Calculate the total amount of deposits
The total amount of deposits is $P\times n$. Here, $P = 7000$ and $n = 25$, so the total amount of deposits is $7000\times25=\$175000$.
## Step4: Calculate the interest
The interest $I$ is the future - value of the annuity minus the total amount of deposits.
$I=F-(P\times n)$.
$I = 412202-175000=\$237202$.
# Answer:
a. $412202$
b. $237202$