Question

You are saving for your child's college tuition. Starting from the birth, you deposit $500 into an account at the beginning of each month. The account generates 0.5% per month. By the time your child is 18 years old, how much money would you have in the account (assuming there are 18*12=216 payments, i.e there is no payment on the day your child turns 18)?

Answer 1

The equal payments at the beginning of each month shall form an annuity due and the money at the time of 18^th birthday shall be the future value of annuity due.

Annuity payment = $500

Monthly interest rate = 0.5% = 0.005

Number of monthly payments = 18 years * 12 = 216

Future value of annuity due = Annuity payment*{(1+r)ⁿ-1}/r * (1+r)

Money in account when child is 18 years old = $500*(1.005²¹⁶-1)/0.005 * 1.005 = $193,676.60*1.005 = $194,644.98