you would like to have $950,000 in 45 years by making regular deposits at the end of each month in an…

you would like to have $950,000 in 45 years by making regular deposits at the end of each month in an annuity that pays 8% compounded monthly. the table below shows the 2021 marginal tax rates, standard deduction, and exemptions for a single person. complete parts (a) through (c)\n| tax rate | single |\n| ---- | ---- |\n| 10% | up to $9950 |\n| 12% | $9951 to $40,525 |\n| 22% | $40,526 to $86,375 |\n| 24% | $86,376 to $164,925 |\n| 32% | $164,926 to $209,425 |\n| 35% | $209,426 to $523,600 |\n| 37% | more than $523,600 |\n| standard deduction | $12,550 |\nclick the icon to view some finance formulas\na. determine the deposit at the end of each month.\nin order to have $950,000 in 45 years, you should deposit $ each month (round up to the nearest dollar)

you would like to have $950,000 in 45 years by making regular deposits at the end of each month in an annuity that pays 8% compounded monthly. the table below shows the 2021 marginal tax rates, standard deduction, and exemptions for a single person. complete parts (a) through (c)\n| tax rate | single |\n| ---- | ---- |\n| 10% | up to $9950 |\n| 12% | $9951 to $40,525 |\n| 22% | $40,526 to $86,375 |\n| 24% | $86,376 to $164,925 |\n| 32% | $164,926 to $209,425 |\n| 35% | $209,426 to $523,600 |\n| 37% | more than $523,600 |\n| standard deduction | $12,550 |\nclick the icon to view some finance formulas\na. determine the deposit at the end of each month.\nin order to have $950,000 in 45 years, you should deposit $ each month (round up to the nearest dollar)

Answer

Explanation:

Step1: Identify the relevant formula

The future - value of an ordinary annuity formula 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 interest rate $i = 8%=0.08$. Since it is compounded monthly, the monthly interest rate $r=\frac{0.08}{12}$. The number of years $t = 45$ years, and the number of months $n=45\times12 = 540$ months, and $F=$950000$. We need to solve the formula for $A$: $A=\frac{F\times r}{(1 + r)^{n}-1}$.

Step2: Calculate $r$

$r=\frac{0.08}{12}\approx0.006667$.

Step3: Calculate $(1 + r)^{n}$

$(1 + 0.006667)^{540}\approx13.937$.

Step4: Calculate $(1 + r)^{n}-1$

$(1 + 0.006667)^{540}-1\approx13.937 - 1=12.937$.

Step5: Calculate $A$

$A=\frac{950000\times0.006667}{12.937}=\frac{6334.65}{12.937}\approx490$.

Answer:

$490$