suppose you want to have $300,000 for retirement in 30 years. your account earns 6% interest. how much would…

Explanation:

Step1: Convert annual rate to monthly rate

The annual interest rate $r = 6%=0.06$. The monthly interest rate $i=\frac{r}{12}=\frac{0.06}{12}=0.005$. The number of periods $n = 30\times12=360$ months. The future - value $FV = 300000$.

Step2: Use the future - value of an ordinary annuity formula

The formula for the future - value of an ordinary annuity is $FV = P\times\frac{(1 + i)^{n}-1}{i}$, where $P$ is the monthly payment. We need to solve for $P$. Rearranging the formula gives $P=\frac{FV\times i}{(1 + i)^{n}-1}$.

Step3: Substitute the values into the formula

Substitute $FV = 300000$, $i = 0.005$, and $n = 360$ into the formula: $(1 + 0.005)^{360}=1.005^{360}\approx6.022575$. Then $(1 + 0.005)^{360}-1\approx6.022575 - 1=5.022575$. And $FV\times i=300000\times0.005 = 1500$. So $P=\frac{1500}{5.022575}\approx298.65$.

Answer:

$298.65$