Question

(Question 3 - 4 marks) Mr X wants to fund his grandsons education. He wants his granson to be able to draw 18,000 in 18 years from now for a period of 5 years. He wants to set up a periodic savings plan to do so. If he makes equal annual payments into a savings account that pays 6% per year, how large must his payments be to ensure that his grandsons education is funded Present Value of annuity 14 * (1- (1/(1+i)^n)) Future Value ((1+1)^n-1)

Answer 1

Amount required after 17 years = Present value of withdrawals

=18000*[1/6% * (1-(1/(1+6%)^5))]

= 75,822.55

Future value of annuity = Periodic Amount*[{(1+i)^n – 1}/i]

75,822.55 = Annual amount*[{(1.06)^17 -1 }/0.06]

75,822.55 = 28.21287976*Annual amount

Annual amount = $2,687.52

Hence, deposits required each year = $2,687.52