A house on Sydney’s North Shore is expected to increase in value at an average rate of 7.5% per annum. How long will it take for a $1 600 000 house to reach $2 400 000?

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Answer 1 · 2018-05-16T07:56:17

After #5.6# years

The value will increase each year based on the value the previous year, so this is exponential growth.

#V = P(1+r)^color(blue)(n)" "rarr# we need to find #n#

#2,400,000 = 1,600,000(1+0.075)^n#

#2400000/1600000 = 1.075^n#

#1.5= 1.075^n" "larr# an exponential equation. Use logs.

#log1.5 = nlog1.075#

#log1.5/log1.075=n#

#n = 5.6# years