Question

A house was valued at $120,000 in the year 1992. The value appreciated to $160,000 by the year 2007.

Answer 1

Answer:

A) 0.0194

B) 1.94%

C) $ 170,000

Step-by-step explanation:

Value of house in 1992 = P = $ 120,000

Value of house in 2007 = S = $ 160,000

Time difference from 1992 to 2007 = 15 years

Part A)

The formula of compound interest is:

$S=P(1+r)^{t}$

P is the original amount i.e. $ 120,000

t is the time in years which is 15 years

S is the amount after t years which is $ 160,000

r is the annual growth rate

Using the values, we get:

$160000=120000(1+r)^{15}\\\\\frac{160000}{120000}=(1+r)^{15}\\\\ \frac{4}{3}=(1+r)^{15}\\\\(\frac{4}{3} )^{\frac{1}{15}}=1+r\\\\ r=(\frac{4}{3} )^{\frac{1}{15}}-1\\\\ r=0.0194$

Thus, the annual growth rate is 0.0194

Part B)

In order to convert a decimal to percentage, simply multiply the decimal by 100.

So, 0.0194 in percentage would be 1.94%

Part C)

We have to find the value of house in 2010 i.e. after 18 years. So t =18

Using the values in the formula, we get:

$S=120000(1+0.0194)^{18}\\\\ S=169584$

Rounded to nearest thousand dollars, the value of the house would be $ 170,000