A bank checks how much of a borrower's gross income would go on debt repayments. The borrower earns $80,000 a year, already pays $800 a month on other debts, and the new mortgage would cost $2,200 a month. What share of gross income would the repayments take?
Correct Answer
C) 45%
Total repayments are $800 + $2,200 = $3,000 a month, or $36,000 a year. $36,000 ÷ $80,000 = 45% of gross income. This is a debt-servicing ratio. In New Zealand, 'debt-to-income' in the Reserve Bank's rules means something else: total debt as a multiple of gross income.
Why This Is the Correct Answer
Total repayments are $800 + $2,200 = $3,000 a month, or $36,000 a year, and $36,000 ÷ $80,000 = 45% of gross income. In New Zealand this is a debt-servicing ratio; the Reserve Bank's debt-to-income limit is a different measure, total debt as a multiple of income.
Why the Other Options Are Wrong
Option A: 33%
33% is the mortgage alone ($26,400 ÷ $80,000); it leaves out the $800 a month already committed to other debts.
Option B: 39%
39% counts only half of the existing $800 a month; all $3,000 a month of repayments must be included.
Option D: 52%
52% would need repayments of about $41,600 a year; the correct total of $36,000 is 45% of income.
Deep Analysis of This Finance Question
Lenders look at affordability in two ways. A servicing view asks what share of income the repayments take, tested at a higher interest rate than today's. The Reserve Bank's debt-to-income (DTI) settings, in force since July 2024, instead compare total debt with gross annual income, for example a loan of 6 times income. The calculation here is a servicing ratio: convert every repayment to the same period, add them, and divide by gross income.
Background Knowledge for Finance
Under the Credit Contracts and Consumer Finance Act 2003 a lender must be satisfied the borrower can repay without substantial hardship, which means assessing income against expenses and existing commitments. Each lender sets its own servicing tests. Separately, the Reserve Bank limits how much lending banks can do at high debt-to-income multiples.
Memory Technique
Remember DEBT: Divide Everything By Total income. Take all monthly debt payments, multiply by 12 for annual amount, then divide by annual gross income. Think of it as 'Every dollar of DEBT needs to be measured against Total income.'
When you see DTI questions, immediately identify all debt components, convert to annual figures using the DEBT formula, then divide by annual income. This systematic approach prevents missing debt components or calculation errors.
Exam Tip for Finance
Always convert all debt payments to the same timeframe (monthly or annual) before calculating. Include ALL debt obligations, not just the proposed mortgage. Double-check your arithmetic by working backwards from your answer.
Real World Application in Finance
First-home buyers earning $80,000 have a car loan and a credit card costing $800 a month. At $2,200 a month the new mortgage would take their total repayments to 45% of gross income. Their adviser suggests clearing the card first, which lowers the ratio and improves their chance of passing the bank's servicing test.
Common Mistakes to Avoid on Finance Questions
- •Leaving existing debts out of the calculation
- •Mixing monthly and annual figures
- •Confusing a repayment ratio with the Reserve Bank's debt-to-income multiple
Related Topics & Key Terms
Key Terms:
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