callan patel is planning to go to graduate school in a program of study that will take three years. callan…

callan patel is planning to go to graduate school in a program of study that will take three years. callan wants to have $9,000 available each year for various school and living expenses. if he earns 5 percent on his money, how much must be deposited at the start of his studies to be able to withdraw $9,000 a year for three years? note: do not round intermediate calculations. round your final answer to the nearest whole number. amount to be deposited

callan patel is planning to go to graduate school in a program of study that will take three years. callan wants to have $9,000 available each year for various school and living expenses. if he earns 5 percent on his money, how much must be deposited at the start of his studies to be able to withdraw $9,000 a year for three years? note: do not round intermediate calculations. round your final answer to the nearest whole number. amount to be deposited

Answer

Explanation:

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

The formula for the present value of an ordinary annuity is $PV = A\times\frac{1-(1 + r)^{-n}}{r}$, where $PV$ is the present value (the amount to be deposited), $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $A=$9000$, $r = 0.05$, and $n = 3$.

Step2: Substitute the values into the formula

$PV=9000\times\frac{1-(1 + 0.05)^{-3}}{0.05}$. First, calculate $(1 + 0.05)^{-3}=\frac{1}{(1 + 0.05)^{3}}=\frac{1}{1.05^{3}}=\frac{1}{1.157625}\approx0.863838$. Then, $1-(1 + 0.05)^{-3}=1 - 0.863838 = 0.136162$. And $\frac{1-(1 + 0.05)^{-3}}{0.05}=\frac{0.136162}{0.05}=2.723248$.

Step3: Calculate the present value

$PV=9000\times2.723248 = 24509.232$.

Answer:

$24509$