Dave and Sharon are a professional couple in their late 30s. They have managed to save a $200,000 deposit for a house worth $1million. They can take out a mortgage for 4.9% per annum for 30 years. Rent growth rate is 2.5% per annum, inflation rate is 2% per annum, and return on investment is 4% per annum. Cost of selling a home is 2.5% of its value, maintenance and insurance is 1.5% per annum. Ignore other costs.

They can rent a similar property for $650 per month.

Dave believes house prices will grow at 4.5% per annum. If he is correct, are they better off buying or renting?

Sharon is less optimistic than Dave, and thinks that house prices will only grow at 1.6% per annum. If she is correct, are they better off buying or renting?

Justify your answer.