Question

Homes in your neighborhood appreciates at a rare Of 3.5% annually. The family purchase a home in your neighborhood with a value of 160,000 at this rate how many years will it take for the home to be valued at 250,000

Answer 1

Answer: it will take 13 years for the home to be valued at 250,000

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the value of the house after t years.

t represents the number of years.

b represents the initial value of the house.

r represents rate of growth.

From the information given,

b = 160000

y = 250000

r = 3.5% = 3.5/100 = 0.035

Therefore

250000 = 160000(1 + 0.035)^t

250000/160000 = (1.035)^t

1.5625 = (1.035)^t

Taking log of both sides to base 10

Log 1.5625 = log1.035^t = tlog1.035

0.1938 = t × 0.0149

t = 0.1938/0.0149

t = 13 years

Answer 2

Answer:

In 13 years the home to be valued at 250,000.

Step-by-step explanation:

Present value of home = 160000

Annual increasing rate of the home = 3.5 %

Final value of home is = 250000

Let this value of  home becomes after t years.

⇒ $250000 = 160000 (\frac{103.5}{100})^{T}$

⇒ 1.5625 = $1.035^{T}$

⇒ ㏑ 1.5625 = T ㏑ 1.035

⇒ T = 13 years

Therefore in 13 years the home to be valued at 250,000.