Fortnightly budget with an irregular bill
Mia works part-time at a Hobart cafe and takes home $1,180 per fortnight after tax. Her regular fortnightly costs are rent $520, groceries $180, transport $60, phone $25 and gym $30. Once a year she pays a $960 car registration bill, and she wants to save $1,500 for a trip in 12 months. She currently has $210 in savings and no other debts. Mia says, 'I'll just put the registration on my credit card when it comes and worry about it then.' Her credit card charges 19.9% per annum on unpaid balances, calculated monthly on the outstanding amount.
1. Work out Mia's fortnightly surplus after her regular costs, then decide how much she must set aside each fortnight to cover the registration bill and reach her trip goal on time.
Read the worked answer
Regular fortnightly costs: 520 + 180 + 60 + 25 + 30 = $815.\nSurplus: 1,180 − 815 = $365 per fortnight.\n\nThere are 26 fortnights in a year.\nRegistration: 960 ÷ 26 ≈ $36.92 per fortnight.\nTrip saving needed: 1,500 − 210 = 1,290; 1,290 ÷ 26 ≈ $49.62 per fortnight.\n\nTotal set-aside: 36.92 + 49.62 ≈ $86.54 per fortnight, leaving about $278 per fortnight of discretionary money. The plan is comfortably achievable, so putting the registration on the card is unnecessary.
2. Suppose Mia instead pays the $960 registration on her credit card and repays it at $100 per month. Using 19.9% per annum charged monthly on the outstanding balance, explain why the debt lasts longer than 9.6 months and estimate the interest cost.
Read the worked answer
Monthly rate = 19.9% ÷ 12 ≈ 1.658%.\nIf there were no interest, 960 ÷ 100 = 9.6 months. But interest is added to the balance each month before the payment, so the balance falls more slowly.\n\nApproximate interest using the average balance: the balance falls from about $960 to about $0 over roughly 11 months, so average balance ≈ $480. Interest ≈ 480 × 0.01658 × 11 ≈ $87.\n\nSo she pays roughly $85–$90 in interest and takes about 11 months, not 9.6. Paying $36.92 per fortnight into a separate account avoids that cost entirely and is the better judgement call.