Question

You and your friend, Polly Horn are thinking of going on a year trip around the world in exactly

3 years’ from today. Unfortunately, you will need a lot of money to ensure you can afford all

the fun activities you have planned! You have determined that you will each need $30,000 to

fund this trip. Polly Horn has been lucky enough to win the lottery recently and can afford to

put a single lump sum into the bank account today. Unfortunately, you are unable to do the

same, and have to place fortnightly payments into the bank account for the next three years,

starting in a fortnight from today. Given this, and the fact that the interest rate available to

both Polly Horn and yourself is 9% p.a. compounded monthly, calculate:

a) The lump sum Polly Horn puts into the bank today; and,

b) The fortnightly payment you have to place into the bank account to have exactly

$30,000 in three years’ time.

Answer 1

a). FV (future value) = 30,000; APR = 9%; n (frequency of compounding p.a.) = 12; N (number of compoundings during the investment period) = 3*12 = 36

Amount to be invested today = FV/(1 + APR/n)^N

= 30,000*(1+9%/12)^36 = 22,924.47

b). Here, the frequency of deposit (m = 52/2 = 26) is different from the frequency of compounding (n = 12), so

effective fornightly rate = [(1 + APR/n)^(n/m)] -1

= [(1+9%/12)^(12/26)] -1 = 0.3455%

Amount to be invested every fortnight: FV = 30,000; PV = 0; N (number of deposits) = 3*26 = 78; rate = 0.3455%; Type = End (or 0), solve for PMT.

Deposit per fortnight = 335.78

Note: This can also be solved using FV of ordinary annuity formula.)