Question

Starting a 5 year double degree at Monash, student services offers a choice between 2 ways of paying for your school fees.

The first choice is for a fixed payments of $30,000 paid at the beginning of each year for 5 years.

The second choice is for a first payment of $25,000 paid at the end of your first year, increasing by 7% each year till your final year.

Using a discount rate of 10% p.a., which should you choose and what is the cost of that choice?

Answer 1

Choice 1:

P = Periodic payment = $30,000

n = 5 yeras

r = 10%

Present value of the choice = P + P[1 - (1+r)^(n-1)]/ r

= $30,000 + $30,000[1 - (1+10%)^(5-1)]/10%

= $30,000 + [$30,000 * 0.31698654463 / 0.10]

= $30,000 + $95095.96339

= $125,095.96

Choice 2:

P = First payment = $25,000

g = growth rate = 7%

n = 5 yeras

r = 10%

Present value of choice = [P / (r-g)] *[1 - ((1+g)/(1+r))^n]

=[$25,000 / (10%-7%)] * [1 - ((1+7%)/(1+10%))^5]

= $833,333.33333 * 0.12912572371

= $107,604.769762

=$107,604.77

Present value of 1st choice is $125,095.96

Present value of 2nd choice is $107,604.77

Therefore, 2nd choice should be selected