jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest…

Explanation:

Step1: Identify the 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 number of periods.

Step2: Calculate the interest rate per period

The annual interest rate $i = 1.75%=0.0175$. Since the interest is compounded monthly, the interest rate per period $r=\frac{0.0175}{12}$.

Step3: Calculate the number of periods

The time is $t = 42$ years. Since the deposits are made monthly, the number of periods $n=42\times12 = 504$.

Step4: Substitute the values into the formula

$A = 100$, $r=\frac{0.0175}{12}$, and $n = 504$. $F=100\times\frac{(1+\frac{0.0175}{12})^{504}-1}{\frac{0.0175}{12}}$ First, calculate $(1+\frac{0.0175}{12})^{504}$. Let $x=\frac{0.0175}{12}\approx0.00145833$. Then $(1 + x)^{504}=(1 + 0.00145833)^{504}$. Using a calculator, $(1 + 0.00145833)^{504}\approx2.0977$. Next, $(1+\frac{0.0175}{12})^{504}-1\approx2.0977 - 1=1.0977$. $\frac{(1+\frac{0.0175}{12})^{504}-1}{\frac{0.0175}{12}}=\frac{1.0977}{0.00145833}\approx752.77$. $F = 100\times752.77=75277$.

Answer:

$75277$