Question

A home was bought in 2000 for $125,000, and its value appreciates by 2.5% every single year. The value of the home t years since 2000 is given by the formula V(t) = 125,000(1.025). Find the value of the home in the year 2018.

a) $164,102.48
b) $162,890.63
c) $161,728.49
d) $160,615.38

Answer 1

Using the formula V(t) = 125,000(1.025)^t, the value of a home bought in 2000 for $125,000 with an annual appreciation of 2.5% comes to approximately $195,119.34 in 2018. None of the multiple-choice options match this result.

Step-by-step explanation:

To calculate the value of a home in the year 2018 that was bought in 2000 for $125,000 and appreciates by 2.5% every year, we use the formula V(t) = 125,000(1.025)^t, where 'V(t)' is the value of the home after 't' years. Since we are looking for the value in 2018, and the home was bought in 2000, we have 't' equal to 2018 - 2000, which is 18 years. Plugging in the numbers:

V(18) = 125,000(1.025)^18

When calculated:

V(18) = 125,000 x (1.025)^18

V(18) = 125,000 x 1.559454687

V(18) ≈ 195,119.34

Therefore, the value of the home in 2018 is approximately $195,119.34. This is not one of the options provided, so there may be a mistake in the original question or the options given.