You invest $1000 in an account. How do you find the value of the accounts after 4 years with a 4.2% interest compounded continuously?

Answer 1

Amount after #4# years will be #1182.94(2dp)#

Formula for continuously compounded amount is #A=P*e^(r/100*t)# ;

P = principal = 100, r = interest rate = 4.2%, t = time = 4 years, e = 2.71828.

#A=1000*2.71828^(4.2/100*4)=1182.94(2dp)#
Amount after #4# years will be #1182.94(2dp)#[Ans]
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the value of the account after 4 years with a 4.2% interest compounded continuously:

  1. Use the continuous compounding formula: A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), t is the time the money is invested for in years, and e is Euler's number (approximately 2.71828).
  2. Substitute the given values into the formula: A = 1000 * e^(0.042 * 4).
  3. Calculate the exponent: e^(0.042 * 4) ≈ e^0.168 ≈ 1.1825.
  4. Multiply the principal amount by the exponent: A ≈ 1000 * 1.1825 ≈ $1182.50.
  5. The value of the account after 4 years with a 4.2% interest compounded continuously is approximately $1182.50.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7