Question

A family starts an education fund for their son Patrick when he is 8 years old, investing $500 on his eighth birthday, and increasing the yearly investment by $500 per year until Patrick is 21 years old. The fund pays 6% annual interest. What is the fund’s future worth after the deposit when Patrick is 21?

Answer 1

The fund’s future worth after the deposit when Patrick is 21 is $8,713,691.01.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FW = C * (((1 + r)^n - (1 + g)^n) / (r - g))

Where;

FW = future worth or future value = ?

C = first deposit = $500

r = annual interest rate = 6%, or 0.06

g = growth rate of investment = Yearly investment increase / First deposit = $500 / $500 = 1

n = number of years = 21 - 8 + 1 = 14

Substituting all the values into equation (1), we have:

FW = $500 * (((1 + 0.06)^14 - (1 + 1)^14) / (0.06 - 1))

FW = $500 * ((1.06^14 - 2^14) / - 0.94)

FW = $500 * (2.26090395575443 - 16,384) / -0.94)

FW = $500 * (-16,381.7390960442 / -0.94)

FW = $500 * 17,427.3820170683

FW = $8,713,691.00853415

Rounding to 2 decimal places, we have:

FW = $8,713,691.01

Therefore, the fund’s future worth after the deposit when Patrick is 21 is $8,713,691.01.