Question

Print Pete Morton is planning to go to graduate school in a program of study that will take three years. Pete wants to have $15,000 available each year for various school and living expenses. If he earns 4 percent on his money, how much must be deposited at the start of his studies to be able to withdraw $15,000 a year for three years? (Exhibit 1-A, Exhibit 1-B, Exhibit 1-C, Exhibit 1-D) Note: Use appropriate factor(s) from the tables provided. Round time value factor to 3 decimal places and final answer to the nearest whole number.

Answer 1

To be able to withdraw $15,000 a year for three years, Pete must deposit $52,336 at the start of his graduate studies.

Pete is planning to go to graduate school for three years and needs $15,000 annually to cover various school and living expenses. To calculate the amount he must deposit at the start of his studies, we need to use the concept of present value and annuities. Since he wants to withdraw $15,000 every year for three years, it can be considered an ordinary annuity.

The formula to find the present value of an ordinary annuity is:

`\[ PV = (PMT)/(r) * (1 - (1)/((1+r)^n)) \]`

Where:

- PV is the present value (the amount to be deposited at the start of studies)

- PMT is the annual payment ($15,000)

- r is the interest rate per period (4% or 0.04 as a decimal)

- n is the number of periods (three years)

Substituting the values into the formula:

`\[ PV = (15,000)/(0.04) * (1 - (1)/((1+0.04)^3)) \]`

Solving this equation gives us the result:

`\[ PV = (15,000)/(0.04) * (1 - (1)/(1.04^3)) \approx 52,336 \]`

So, Pete needs to deposit $52,336 at the start of his graduate studies to be able to withdraw $15,000 a year for three years. This will ensure that he has enough funds to cover his expenses throughout his time in the graduate program.