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 $13,500 available each year for various school and living expenses. if he earns 6 percent on his money, how much must be deposited at the start of his studies to be able to withdraw $13,500 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 $13,500 available each year for various school and living expenses. if he earns 6 percent on his money, how much must be deposited at the start of his studies to be able to withdraw $13,500 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 formula for present - value of an ordinary annuity

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.

Step2: Define the values of $A$, $r$, and $n$

$A=$13500$, $r = 0.06$ (6% expressed as a decimal), and $n = 3$ years.

Step3: Substitute the values into the formula

$PV=13500\times\frac{1-(1 + 0.06)^{-3}}{0.06}$. First, calculate $(1 + 0.06)^{-3}=\frac{1}{(1 + 0.06)^{3}}=\frac{1}{1.06^{3}}=\frac{1}{1.191016}\approx0.839619$. Then, $1-(1 + 0.06)^{-3}=1 - 0.839619 = 0.160381$. $\frac{1-(1 + 0.06)^{-3}}{0.06}=\frac{0.160381}{0.06}\approx2.67301$. $PV = 13500\times2.67301=36085.635$.

Step4: Round the final answer

Rounding to the nearest whole number, $PV\approx36086$.

Answer:

36086