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

Answer:

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

Step-by-step 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 = $(\frac{F}{P})^{\frac{1}{n}}$

Or, r = $(\frac{120,000}{30,000})^{\frac{1}{40}}$

Or, r = $4^{\frac{1}{40}}$

∴  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