1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notsponge [240]
3 years ago
8

If you invest $1000 at an interest rate of 2.5% compounded continuously, calculate how many years. How long will it take for you

r investment to double?
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
5 0

Answer:

It will take about 27.7 years

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

∵ The invest is $ 1000

∴ P = 1000

∵ The interest rate is 2.5%

∴ r = 2.5/100 = 0.025

- They ask about how long will it take to make double the investment

∴ A = 2 × 1000 = 2000

∵ A = P e^(rt)

∴ 2000 = 1000 (e)^(0.025t) ⇒ divide both sides by 1000

∴ 2000/1000 = e^(0.025t)

∴ 2 = e^(0.025) ⇒ take ln for both sides

∴ ln(2) = ln[e^(0.025t)]

∵ ln(e)^n = n

∴ ln(2) = 0.025t ⇒ divide both sides by 0.025

∴ t = ln(2)/0.025 = 27.7 years

* It will take about 27.7 years

You might be interested in
Would appreciate any help!! :D
Salsk061 [2.6K]
73+112+90=275
360-275=85
the angle of x is 85 degrees
(pls mark brainliest)
6 0
2 years ago
Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.
Hoochie [10]

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

    2^{n}>n

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

      2^{k}>k

                   ---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement  is true for, n=k+1.

     \rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

      2^{k}>k

                 

   

3 0
3 years ago
Find the absolute value of 16
myrzilka [38]

Answer:

16

Step-by-step explanation:

Absolute value always means positive i.e to remove any negative signs in front of a number.

Since 16 is a simple digit with the  as the positive sign is  invincible.

So, the absolute value of 16 is 16.

5 0
2 years ago
Read 2 more answers
SOLVE QUICK PLEASE!! 20 POINTS
PolarNik [594]

Answer:

SA = 384 in²

Step-by-step explanation:

Assuming we're finding surface area:

SA of top of large cube: 8(8) - 4(4) = 48 in²

SA of sides of large cube: 4(8)(8) = 256 in²

SA of exposed faces of small cube: 5(4)(4) = 80 in²

Total = 48 + 256 + 80 = 384 = ∑SA

6 0
2 years ago
Hey ! Can anyone help me solve these problems please. Thank you !
Bas_tet [7]
There are 3 sides to the 360 degree circle. This mean by dividing 360 by 120 = . This mean the answer would be 120 degrees per chunk of the circle. Hope this helps.
6 0
2 years ago
Other questions:
  • Algebraic equation of 185 is less than a number
    13·1 answer
  • (-2,12) (1,1) what would the anwser be ?​
    10·2 answers
  • What’s the answer this is hard
    9·1 answer
  • The equation y = 4x represents the relationship between time, x, and distance traveled, y. Which table represents this relations
    10·1 answer
  • I will give Brainliest to who answers. 9a + 46 = 5a + 74
    13·1 answer
  • Can someone help me w this?​
    6·2 answers
  • Please help me with this i will give brainliest
    11·1 answer
  • Mrs. Harris took 6 oranges out of the refrigerator and cut them into wedges, each wedge represents 1/6 of the entire orange. Her
    13·1 answer
  • 1.5 x 10 to the power of 11
    13·2 answers
  • Please Help!!!!!!!!!!!!!!!!!!!!!<br> Will mark BRAINLIEST
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!