question 3 suppose $2,500 is deposited into an account each quarter. the account grows at an annual rate of…

Explanation:

Step1: Identify the relevant 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 amount of each payment, $r$ is the interest rate per period, and $n$ is the total number of periods. The annual interest rate $i = 7.4%=0.074$. Since it is compounded quarterly, the interest rate per period $r=\frac{0.074}{4}=0.0185$. The number of years $t = 25$ years. Since there are 4 quarters in a year, the total number of periods $n=25\times4 = 100$. The amount of each payment $A = 2500$.

Step2: Substitute the values into the formula

$F=2500\times\frac{(1 + 0.0185)^{100}-1}{0.0185}$. First, calculate $(1 + 0.0185)^{100}$. Using the formula $a^{b}$, where $a = 1.0185$ and $b = 100$, we get $(1.0185)^{100}\approx5.9177$. Then, $(1.0185)^{100}-1\approx5.9177 - 1=4.9177$. $\frac{(1.0185)^{100}-1}{0.0185}=\frac{4.9177}{0.0185}\approx265.8216$. Finally, $F = 2500\times265.8216=664554$.

Answer:

664554