Question

In order to buy an authentic Wookie mask,, Dale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. How long will it take until Dale car
buy this mask? Round your answer to the nearest hundredth.
years

Answer 1

It will take 7.30 years until Dale can by his mask

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

$A=Pe^{rt}$ , where

• 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

Dale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. We need to find how long will it take Dale until can buy this mask

∵ Dale invests $6000

∴ P = 6000

∵ The interest rate is 9.5% ⇒ compounded continuously

∴ r = 9.5% = 9.5 ÷ 100 = 0.095

∵ The mask costs $12000

∴ A = 12000

Substitute these values in the formula above

∵ $12000=6000e^{0.095t}$

- Divide both sides by 6000

∴ $2=e^{0.095t}$

- Insert ㏑ for both sides

∴ $ln(2)=ln(e^{0.095t}$)

- Remember that $ln(e^{n})=n$

∴ $ln(2)=0.095t$

- Divide both sides by 0.095

∴ t = 7.29628611

∴ t = 7.30 ⇒ to the nearest hundredth year

It will take 7.30 years until Dale can by his mask

Learn more:

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