Home Loan Calculator

NZ Home Loan Calculator

NZ Home Loan Calculator

Example :

If the repayment frequency is weekly, let’s confirm the calculation for a $1,000 loan at a 10% annual interest rate over 1 year.


Key Inputs:

  • Loan Amount: $1,000
  • Annual Interest Rate: 10% (0.10)
  • Loan Term: 1 year
  • Repayment Frequency: Weekly (52 payments per year)

Formula for Fixed Repayments:

The formula remains the same: M=P⋅r1−(1+r)−nM = \frac{P \cdot r}{1 – (1 + r)^{-n}}

Where:

  • MM: Weekly repayment amount
  • PP: Loan amount ($1,000)
  • rr: Weekly interest rate (0.10/52=0.00192310.10 / 52 = 0.0019231)
  • nn: Total number of payments (5252)

Step-by-Step Calculation:

  1. Weekly Interest Rate (rr): r=0.10/52=0.0019231r = 0.10 / 52 = 0.0019231
  2. Total Number of Payments (nn): n=52 weeks in 1 year.n = 52 \text{ weeks in 1 year.}
  3. Weekly Repayment Amount (MM): M=1000⋅0.00192311−(1+0.0019231)−52M = \frac{1000 \cdot 0.0019231}{1 – (1 + 0.0019231)^{-52}} Simplifying: M=1.92311−(1.0019231)−52M = \frac{1.9231}{1 – (1.0019231)^{-52}} M=1.92311−0.904837M = \frac{1.9231}{1 – 0.904837} M=1.92310.095163M = \frac{1.9231}{0.095163} M=20.23 (NZD/week).M = 20.23 \text{ (NZD/week).}
  4. Total Repayment: 20.23×52=1,051.96 (NZD).20.23 \times 52 = 1,051.96 \text{ (NZD).}
  5. Total Interest Paid: 1,051.96−1,000=51.96 (NZD).1,051.96 – 1,000 = 51.96 \text{ (NZD).}

Results (Weekly Repayment):

  • Repayment Amount per Payment: NZD 20.23
  • Total Repayment: NZD 1,051.96
  • Total Interest Paid: NZD 51.96