Dr. Stein has just invested $10,000 for his son (age 7). The money will be used for his son's education 15 years from now. He calculates that he will need $100,000 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal?

Question

Quizplus · Accepted Answer

We can use the formula for future value of a single sum to solve the problem:

FV = PV x (1+r)^n

where: 
FV = future value 
PV = present value (or the amount invested now) 
r = rate of return 
n = number of periods (in this case, 15 years)

We are given PV, FV, and n, so we can solve for r:

$100,000 = $10,000 x (1+r)^15

Divide both sides by $10,000:

10 = (1+r)^15

Take the 15th root of both sides:

1.1618 = 1+r

Subtract 1 from both sides:

r = 0.1618 or 16.18%

Therefore, Dr. Stein will need to achieve a rate of return of approximately 16% to reach his goal of $100,000 in 15 years. The closest choice is B.

Dr Stein Has Just Invested $10,000 for His Son (Age