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?
Amount after
P = principal = 100, r = interest rate = 4.2%, t = time = 4 years, e = 2.71828.
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To find the value of the account after 4 years with a 4.2% interest compounded continuously:
- 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).
- Substitute the given values into the formula: A = 1000 * e^(0.042 * 4).
- Calculate the exponent: e^(0.042 * 4) ≈ e^0.168 ≈ 1.1825.
- Multiply the principal amount by the exponent: A ≈ 1000 * 1.1825 ≈ $1182.50.
- The value of the account after 4 years with a 4.2% interest compounded continuously is approximately $1182.50.
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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.

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