Answer:
It is worth $54,664 after 5 years
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
[tex]A=Pe^{rt}[/tex]
- 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
∴ [tex]A=(30,000)e^{(0.12)(5)}[/tex]
∴ [tex]A=(30,000)e^{0.6}[/tex]
∴ A = 54663.56401 dollars
- Round it to the nearest dollar
∴ A = 54,664 dollars
It is worth $54,664 after 5 years
