a. use the appropriate formula to find the value of the annuity. b. find the interest. periodic deposit…

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.)

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. $237202$