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 rate time $7000 at the end of each year 6.5% compounded annually 25 years i 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
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 deposit, $r$ 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 $(1 + 0.065)^{25}$.
$(1 + 0.065)^{25}=1.065^{25}\approx4.46774$.
Then, $(1.065)^{25}-1\approx4.46774 - 1=3.46774$.
$\frac{(1.065)^{25}-1}{0.065}=\frac{3.46774}{0.065}\approx53.34985$.
$F = 7000\times53.34985=\$373448.95$.
## Step3: Find the interest
The total amount of deposits made over 25 years is $P\times n=7000\times25=\$175000$.
The interest $I=F - P\times n$.
$I = 373448.95-175000=\$198448.95\approx\$198449$.
# Answer:
a. $\$373449$
b. $\$198449$