Question

Matt purchased a new car for $30,000. The car depreciates approximately 12% of its value each year compounded continuously.. How much is it worth after 5 years? Round the answer to nearest dollar.

Answer 1

Answer:

It is worth $54,664 after 5 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

$A=Pe^{rt}$  

• A is the future value of the investment, including interest
• P is the principal investment amount (the initial amount)
• r is the interest rate in decimal  
• t is the time the money is invested for

∵ Matt purchased a new car for $30,000

∴ P = 30,000

∵ The car depreciates approximately 12% of its value each year

   compounded continuously

∴ r = 12%

- Change it to decimal by divide it by 100

∴ r = 12 ÷ 100 = 0.12

∵ t = 5 years

- Substitute all of these values in the formula above

∴ $A=(30,000)e^{(0.12)(5)}$

∴ $A=(30,000)e^{0.6}$

∴ A = 54663.56401 dollars

- Round it to the nearest dollar

∴ A = 54,664 dollars

It is worth $54,664 after 5 years