Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period.=P$10,000, =t112 yr
(a) 1% interest
(b) 4% interest
(c) 4.5% interest
Answers
Answer: (a )$30648.54 (b)$882,346.73 (c) $1,544,700.15
Step-by-step explanation:
Formula: , where P= principal , r=rate of interest, t= time
Given : P= $10,000, t = 112 years
(a) r = 1% = 0.01
Hence, Amount = $30,648.54
(b) r = 4% = 0.04
Hence, Amount = $882,346.73
(c) r = 4.5% = 0.045
Hence, Amount = $1,544,700.15
Final answer:
For 1% interest, the investment will be worth $10100.50. For 4% interest, it will be worth $10420.96, and for 4.5% interest, it will be worth $10451.65.
Explanation:
To determine the amount that an investment is worth at the end of a given time period with continuous compounding, we can use the formula A = P * e^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the time in years.
(a) For 1% interest:
A = 10000 * e^(0.01 * 1) = $10100.50
(b) For 4% interest:
A = 10000 * e^(0.04 * 1) = $10420.96
(c) For 4.5% interest:
A = 10000 * e^(0.045 * 1) = $10451.65
Learn more about Continuous compounding here:
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Which of these is logically equivalent to the given statement? (1 point)
1. If Amelia did not go to the park, then she did not finish her homework.
2. If Amelia did not finish her homework, then she will go to the park.
3. If Amelia goes to the park, then she did not finish her homework.
4. If Amelia finishes her homework, then she cannot go to the park.
Answers
Hello there.
In this problem, we can use our intuition of logic, but I will show a proof of the result in a truth table later. Then, let's get started!
Given:
→ Amelia finishes the homework (sentence H, can be True or False)
→ Amelia goes to the park (P, true or false)
Then, we have: If H, then P. Logically:
H ⇒ P
Then we can think: everytime she does the homework, she goes to the park. Therefore, if she did not go to the park, she will not have finished the homework (It is an equivalent sentence).
Alternative 1.
==========
Now, let's prove that (H ⇒P) is equivalent to (¬P ⇒ ¬H), via the truth table:
H P ¬H ¬P (H ⇒ P) (¬P ⇒ ¬H)
T T F F T T
T F F T F F
F T T F T T
F F T T T T
As we can see, the results are identical, therefore, the sentences are indeed equivalent.
I hope it hepls :)
Answers
Answers
Answer:given by what?
Answers
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
Answer:
It's A: -288
Step-by-step explanation:
on edge 2021
Answers
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