you put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly…

Answer:

D. $3,832.84

Explanation:

Step1: Identify the formula for future - value of an ordinary annuity

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 is $i = 2.5%=0.025$. Since it is compounded monthly, the interest rate per period $r=\frac{0.025}{12}$.

Step3: Calculate the number of periods

The investment is for 23 years. Since there are 12 months in a year, the number of periods $n = 23\times12=276$.

Step4: Substitute the values into the formula

$A = 125.32$, $r=\frac{0.025}{12}$, and $n = 276$. [ \begin{align*} F&=125.32\times\frac{(1+\frac{0.025}{12})^{276}-1}{\frac{0.025}{12}}\ \end{align*} ] First, calculate $(1+\frac{0.025}{12})^{276}\approx1.7677$. Then $(1+\frac{0.025}{12})^{276}-1\approx0.7677$. And $\frac{(1+\frac{0.025}{12})^{276}-1}{\frac{0.025}{12}}\approx\frac{0.7677}{\frac{0.025}{12}}\approx36.8976$. Finally, $F = 125.32\times36.8976\approx3832.84$.