Question

Howard wishes to establish a university fund for his daughter who is currently 7 years old.

Required:

a. If his daughter will need a monthly income of $700, how much does he need to be in place at the start of his university life (i.e. start of first-year) so that the $700 per month is achievable? Assuming that the interest over the three years while his daughter is at university is 6%p.a. compounded monthly and she is paid the $700 at the start of the month for this present value annuity

b.  Using your answer from part a, how much does Howard need to invest now as a lump sum (present value) for the next 11 years at 5%pa (compounded annually) so that there are sufficient funds to achieve the amount from part a.

Answer 1

Annuity paid at Beginning = 700

Rate per month (I)= 6%/12= 0.005

Number of months (n) in 3 years = 3*12= 36

Present value of Annuity due = P + (P*(1-(1/(1+I)^(n-1)))/I

=700 + (700*(1-(1/(1+0.005)^(36-1)))/0.005)

=23124.76

So amount of fund Required at start of University is $23124.76

B.

Future value (needed fund)= 23124.76

Total months in 11 years (11*12) =132

Interest rate per month (I)= 5%/12=0.004166666667

Present value of future value = future value/(1+I)^n

=23125.76/(1+0.004166666667)^132

=13357.6574

So we have to deposit $13357.66 today