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

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.)

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$