marianne opened a retirement account that has an apr of 5.5%. she is planning to retire in 25 years. how…

marianne opened a retirement account that has an apr of 5.5%. she is planning to retire in 25 years. how much should she put into the account each month so that she will have $500,000 when she retires? rounded to the nearest dollar.

marianne opened a retirement account that has an apr of 5.5%. she is planning to retire in 25 years. how much should she put into the account each month so that she will have $500,000 when she retires? rounded to the nearest dollar.

Answer

Explanation:

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

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $F$ is the future value of the annuity, $A$ is the amount of each payment, $r$ is the interest rate per period, and $n$ is the number of periods. The annual percentage rate (APR) is $5.5%=0.055$. The interest rate per month $r=\frac{0.055}{12}$. The number of years is 25, so the number of months $n = 25\times12=300$, and $F = 500000$. We need to solve the formula for $A$: [A=\frac{F\times r}{(1 + r)^{n}-1}]

Step2: Substitute the values into the formula

[r=\frac{0.055}{12}\approx0.004583] [(1 + r)^{n}=(1 + 0.004583)^{300}] Using a calculator, $(1 + 0.004583)^{300}\approx3.8477$. [A=\frac{500000\times0.004583}{3.8477 - 1}] [A=\frac{2291.5}{2.8477}] [A\approx804.75]

Answer:

$805$