Answer:
The answer is approximately 3 years ⇒ answer B
Step-by-step explanation:
* Lets talk about the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
# A = the future value of the investment, including interest
# P = the principal investment amount (the initial amount)
# r = the interest rate
# t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the
principal.
- If you want to calculate the compound interest only, you need
to deduct the principal from the result.
- So, your formula is:
Compounded interest only = Pe^(rt) - P
* Now lets solve the problem
∵ P = $ 6000
∵ A = $ 8000
∵ r = 9/100 = 0.09
∵ t = ?
∵ A = P e^(r t)
∴ 8000 = 6000 e^(0.09 × t) ⇒ divide both sides by 6000
∴ 4/3 = e^(0.09 × t) ⇒ insert ㏑ for both sides
∴ ㏑(4/3) = ㏑ e^(0.09 × t) ⇒ (㏑e = 1)
∴ ㏑(4/3) = 0.09 t ⇒ divide the both sides by 0.09
∴ t = [㏑(4/3)] ÷ 0.09 = 3.196467 ≅ 3 years
