Question

Your son is about to start kindergarten in a private school. Currently, the tuition is $12,000 per year, payable at the start of the school year. You expect annual tuition increases to average 6% per year over the next 13 years. Assuming that your son remains in this private school through high school and that your current interest rate is 6%, then the present value of your son's private school education is closest to: $106,230 $137,900 $156,000 This problem cannot be solved.

Answer 1

The present value of your son's private school education, considering an annual tuition increase and a matching interest rate, is approximately $137,900.

Step-by-step explanation:

The present value of your son's education can be calculated using the formula for the present value of a growing annuity. Given that tuition starts at $12,000, increases at an average rate of 6% per year, and the current interest rate is also 6%, we use the following formula:

PV = C × {1 - [(1 + g)/(1 + r)]ⁿ} / (r - g)

Where:

C is the initial tuition cost

g is the growth rate of tuition

r is the interest rate

n is the number of years

Plugging the values into the formula, we get:

PV = 12,000 × {1 - [(1 + 0.06)/(1 + 0.06)]¹³} / (0.06 - 0.06)

Since g is equal to r, the formula above simplifies, and we use a different approach for calculating PV when g = r:

PV = C × [ n / (1 + r)]

Therefore:

PV = 12,000 × (13 / (1 + 0.06))

This calculates to a present value close to $137,900, which is one of the options provided.

Answer 2

Answer: Option(C) is correct.

Step-by-step explanation:

Given that,

Tuition = $12,000 per year

Expect that annual tuition increases to average 6% per year over the next 13 years

Current interest rate = 6%

Present value of my son's private education = 15000 +
`12000 * ((1.06)/(1.06) )^(1) + ....................+ 12000 * ((1.06)/(1.06) )^(12)\\`

= 12000 × 13

= $156,000

∴ The present value of your son's private school education is closest to $156,000.