find the savings plan balance after 4 years with an apr of 4% and monthly payments of $300. the balance is $…

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 payment per period, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Calculate the interest rate per period

The annual percentage rate (APR) is $4%=0.04$. Since the payments are made monthly, the interest rate per period $r=\frac{0.04}{12}$.

Step3: Calculate the number of periods

The time is 4 years. Since there are 12 months in a year, the number of periods $n = 4\times12=48$.

Step4: Substitute the values into the formula

We have $P = 300$, $r=\frac{0.04}{12}$, and $n = 48$. [ \begin{align*} F&=300\times\frac{(1+\frac{0.04}{12})^{48}-1}{\frac{0.04}{12}}\ &=300\times\frac{(1+\frac{0.04}{12})^{48}-1}{\frac{0.04}{12}}\ &=300\times\frac{(1 + 0.00333\cdots)^{48}-1}{0.00333\cdots}\ \end{align*} ] First, calculate $(1 + 0.00333\cdots)^{48}$. Using the formula $a^{b}$, where $a = 1+\frac{0.04}{12}\approx1.00333$ and $b = 48$, we get $(1.00333)^{48}\approx1.17327$. Then, $(1.00333)^{48}-1\approx0.17327$. $\frac{(1.00333)^{48}-1}{0.00333}\approx\frac{0.17327}{0.00333}\approx52.033$. $F = 300\times52.033=15609.91$.

Answer:

$15609.91$