Exponential Equations 21

Question

A house was valued at $120,000 in the year 1995. The value appreciated to $145,000 by the year 2002.Use the compund interest formula  to answer the following questions.

A) What was the annual growth rate between 1995 and 2002? = ____ Round the growth rate to 4 decimal places.

B) What is the correct answer to part A written in percentage form? =___  %

.C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2007 ?value =____ $  Round to the nearest thousand dollars.

Answer 1

145/120 = (1+r)^7 $120K in 1995, up to $145K in 2002

(1+r)^7 = 24/19

1+ r = 7th root of 24/19

r = (24/19)^(1/7) -1

r = about 0.0339

= 3.39%

in 2007, 5 years later

FV = 19000(1.0339 )^12 = about $283,583.25

= $284,000 rounded to nearest 1,000 dollars