suppose you want to have $500,000 for retirement in 20 years. your account earns 8% interest. how much would…

Explanation:

Step1: Convert annual - interest rate and years to monthly values

The annual interest rate $r = 8%=0.08$, so the monthly interest rate $i=\frac{0.08}{12}$. The number of years $n = 20$, and the number of months $t=20\times12 = 240$. The future - value of the annuity $FV = 500000$.

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

The formula for the future - value of an ordinary annuity is $FV = P\times\frac{(1 + i)^{t}-1}{i}$, where $P$ is the monthly payment. We need to solve for $P$. First, rewrite the formula for $P$: $P=\frac{FV\times i}{(1 + i)^{t}-1}$. Substitute $FV = 500000$, $i=\frac{0.08}{12}$, and $t = 240$ into the formula. $(1+\frac{0.08}{12})^{240}\approx4.9268$. $P=\frac{500000\times\frac{0.08}{12}}{4.9268 - 1}$. $P=\frac{\frac{40000}{12}}{3.9268}$. $P=\frac{40000}{12\times3.9268}\approx843.22$.

Answer:

$843.22$