Question

7. I need help with question in the attached picture!

Answer 1

Given:

Principal amount =P=6000$

Required amount =A=8000$

Rate of compunded interest;r=9%=0.09

Let the number of years be 'n'

So.

A=P(1+r)^t

=> 8000 =6000 (1+0.09)^t

=>8000/6000 =(1.09)^t

=> 8/6 =4/3=1.999.. = (1.09)^t

=> (1.09)^t =1.999≈2

(After using calculator)

(1.09)^3 =1.2950...

(1.09)^9 =2.17189...

So approximately The Time in years required is 9 years... i.e option c.

Hope it helps...

Regards,

Leukonov/Olegion.

Answer 2

The answer is approximately 3 years ⇒ answer B

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