question 3 (12.5 points)\nben purchased a truck for $38,000. the truck depreciates at a rate of 18% per…

question 3 (12.5 points)\nben purchased a truck for $38,000. the truck depreciates at a rate of 18% per year. after 5 years, ben decides to sell the truck. which of the following is the correct depreciation schedule for bens truck and its value after 5 years?\n\na) year 1: $30,000, year 2: $24,600, year 3: $20,172, year 4: $16,541.04, year 5: $13,573.65; value after 5 years: $13,573.65\n\nb) year 1: $29,520, year 2: $24,206.40, year 3: $19,849.25, year 4: $16,276.38, year 5: $13,346.63; value after 5 years: $13,346.63\n\nc) year 1: $31,160, year 2: $25,551.20, year 3: $20,951.98, year 4: $17,180.62, year 5: $14,088.11; value after 5 years: $14,088.11\n\nd) year 1: $30,012, year 2: $24,609.84, year 3: $20,180.07, year 4: $16,547.66, year 5: $13,569.08; value after 5 years: $13,569.08

question 3 (12.5 points)\nben purchased a truck for $38,000. the truck depreciates at a rate of 18% per year. after 5 years, ben decides to sell the truck. which of the following is the correct depreciation schedule for bens truck and its value after 5 years?\n\na) year 1: $30,000, year 2: $24,600, year 3: $20,172, year 4: $16,541.04, year 5: $13,573.65; value after 5 years: $13,573.65\n\nb) year 1: $29,520, year 2: $24,206.40, year 3: $19,849.25, year 4: $16,276.38, year 5: $13,346.63; value after 5 years: $13,346.63\n\nc) year 1: $31,160, year 2: $25,551.20, year 3: $20,951.98, year 4: $17,180.62, year 5: $14,088.11; value after 5 years: $14,088.11\n\nd) year 1: $30,012, year 2: $24,609.84, year 3: $20,180.07, year 4: $16,547.66, year 5: $13,569.08; value after 5 years: $13,569.08

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay depreciation is $V = P(1 - r)^n$, where $P$ is the initial price, $r$ is the rate of depreciation, and $n$ is the number of years. Here, $P=$38000$, $r = 0.18$, and we will calculate the value for each year.

Step2: Calculate the value after Year 1

$V_1=38000\times(1 - 0.18)=38000\times0.82=$31160$

Step3: Calculate the value after Year 2

$V_2 = V_1\times(1 - 0.18)=31160\times0.82=$25551.20$

Step4: Calculate the value after Year 3

$V_3 = V_2\times(1 - 0.18)=25551.20\times0.82=$20951.984\approx$20951.98$

Step5: Calculate the value after Year 4

$V_4 = V_3\times(1 - 0.18)=20951.98\times0.82=$17180.6236\approx$17180.62$

Step6: Calculate the value after Year 5

$V_5 = V_4\times(1 - 0.18)=17180.62\times0.82=$14088.1084\approx$14088.11$

Answer:

C. Year 1: $31,160, Year 2: $25,551.20, Year 3: $20,951.98, Year 4: $17,180.62, Year 5: $14,088.11; Value after 5 years: $14,088.11