Question

John is planning to go to graduate school in a program that will take three years. John wants to have available $10,000 available each year for his school and living expenses.

If he earns 6% on his investments, how much must be deposited at the start of his studies for him to withdraw $10,000 a year for three years?

a) $10,000
b) $29,100
c) $30,000
d) $18,390

Answer 1

d) $18,390

Explanation:

Let X be the amount of money he deposited on the first year of his study.

The question says that he earns 6% on his investment without specifying the investment return time. However, normally it's annually, so let's assume his earning is 6% per annum.

Given that he did not make any withdrawal until the end of the first year, in 2nd year, he'll get the earning of his investment minus 10,000 to pay for his first year study

2nd year Y = X(1.06 ) - 10000

The same goes with 3rd year

3rd year Z = Y(1.06) - 10000

In worst case scenario, let's assume all of the money is used up at the end of third year

Z = 0

Y(1.06) - 10000 = 0

Substitute the first year into the equation:

Y(1.06) - 10000 = 0

(X(1.06)-10000)1.06 -10000 = 0

(1.06^2)X -1.06(10000) - 10000 = 0

X = (10000+10600)/1.06^2 = 18333.92

So the minimum deposit he needs to make to survive for the whole 3 years is $18333.92.

From the answer selection, the nearest value is d) $18,390