Question

A house increases in value from $30,000 to $120,000 over a period of 40 years. Solve by using the formula r = (F/P) to the 1/n power

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Answer 1

The rate at which the value of house increases in 40 years is 1.03

Explanation:

The initial value of house = P = $30,000

The final value of house = F = $120,000

The period for which the value increase = 40 years

Let the rate at which the value increases in 40 years = r%

Now, According to question

The final value of house after n years = The initial value of house ×
`(rate)^(time)`

i.r F = P ×
`(r)^(n)`

Or, r =
`((F)/(P))^{(1)/(n)}`

Or, r =
`((120,000)/(30,000))^{(1)/(40)}`

Or, r =
`4^{(1)/(40)}`

∴ r = 1.03

The rate at which the value increases in 40 years = r = 1.03

Hence,The rate at which the value of house increases in 40 years is 1.03 Answer