Question

The value of an investment property after t years can be found using the formula V =C (1 + r)^2, where V is the current

value of the property, C is the original investment,
and r is the annual rate of appreciation.
a. Solve the formula for r.
b. Lew bought a condo 20 years ago for $50,000, and the current value of the condo is $175,000. Assuming the same
rate each year, what has the annual rate of appreciation been? Round your answer to the nearest half a percent.

Answer 1

0.871

Explanation:

a. Solve the formula for r.

V = C (1 + r)²

dividing both sides by C, we have

V/C = (1 + r)²

(1 + r)² = V/C

taking square root of both sides, we have

√(1 + r)² = √(V/C)

1 + r = √(V/C)

r = √(V/C) - 1

b. Lew bought a condo 20 years ago for $50,000, and the current value of the condo is $175,000. Assuming the same

rate each year, what has the annual rate of appreciation been? Round your answer to the nearest half a percent.

Since r = √(V/C) - 1 and V = $ 175,000 and C = $ 50,000

Substituting the values of the variables into the equation for r, we have

r = √($ 175,000/$ 50,000) - 1

r = √3.5 - 1

r = 1.871 - 1

r = 0.8708

r ≅ 0.871