Respuesta :
Answer:
Step-by-step explanation:
2x=x(1.07)^t
2=(1.07)^t
t=log2/(log 1.07) ≈10.2 4 years
so it doubles in approximately in 10.2 years
To solve the problem we must know about Compounding.
What is compounding?
Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A = P(1+r)^t[/tex]
where A is the value after t period of time,
P is the value of the asset at the beginning, and,
r is the rate of interest.
The value of the home doubles once each decade.
Given to us
- The value of a home increases by 7% each year.
As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.
We know the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Why does the value doubles?
Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Substitute the rate at which the value is increasing,
[tex]A = P(1+0.07)^t[/tex]
We know that in a decade there are 10 years,
[tex]A = P(1.07)^{10}[/tex]
[tex]A = 1.967P\approx 2P[/tex]
As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.
Hence, the value of the home doubles once each decade.
Learn more about Compounding:
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