Question

Michelle wishes to establish a university fund for her son who is currently 8 years old.

Required:

a. If her son will need a monthly income of $900, how much does he need to be in place at the start of his university life (ie start of first-year) so that the $900 per month is achievable? Assuming that the interest over the three years while her son is at university is 6%p.a. compounded monthly and he is paid the $900 at the start of the month for this present value annuity.

b. Using your answer from part a, how much does Michelle need to invest now as a lump sum (present value) for the next 10 years at 5%pa (compounded annually) so that there are sufficient funds to achieve the amount from part a.

Answer need to be discussed in details.

Answer 1

a]

PV of annuity due = P + [P * [1 - (1 + r)^-(n-1)] / r]

where P = periodic payment. This is $900

r = interest rate per period. This is (6%/12), or 0.5%

n = number of periods. This is 3*12 = 36.

PV of annuity due = $900 + [$900 * [1 - (1 + 0.5%)^-(36-1)] / 0.5%]

PV of annuity due = $29,731.83

The amount required at the start of university life is $29,731.83

b]

future value = present value * (1 + rate)^{number of years}

$29,731.83 = present value * (1 + 5%)¹⁰

present value = $18,252.77

Amount to invest now = $18,252.77