Question

Based on her past experiences, a homeowner estimates that appliances lose 35% of their resale value each year. If her estimate is accurate, how much will an appliance currently valued at $1,200 be worth in 8 years?If necessary, round your answer to the nearest cent.

Answer 1

Given data,

The principal, P = 1,200

The time, T = 8 years

The amount is calculated by the formula,

$\text{Amount = P(1-}\frac{R}{100})^T$

Put the given values in the formula,

$\begin{gathered} \text{Amount = 1,200 (1-}\frac{35}{100})^8 \\ \text{Amount = 1,200 (}\frac{65}{100})^8 \\ \text{Amount = 1,200}\times\text{ (0.65})^8 \\ \text{Amount = 1},200\times0.03186 \end{gathered}$

Thus, the amount is

$\text{Amount = 38.24}$

Therefore, the current value of the appliance is 38.24