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The simplest way — if your deposit is 20% or more of the property value (LVR 80% or below), LMI doesn't apply. On a $750,000 property, that's a $150,000 deposit. It takes longer to save but eliminates the $15,000–$30,000 LMI cost entirely.
Saving a 20% deposit saves the most in total because you avoid LMI entirely and start with lower repayments. However, the First Home Guarantee scheme gets you into the property market sooner, which can matter in a rising market.
Some combinations work — for example, a guarantor loan with a smaller deposit. But the First Home Guarantee and guarantor loans are typically alternatives rather than combined strategies.
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