Answer:
- 1. <em>For the amount to double</em>: <u>9.37 years</u>
- 2. <em>For the amount to triple</em>: <u>14.85 years</u>
Explanation:
The equation for continuosly compounded interest is:
Where:
- P is the amount that you invest today: $1,300
- F is the value after t years: the double or triple of $1,300
- r is the annual interest rate: 0.074
<u>1. For the amount to double:</u>
Substitute the values and solve for t:
![2\times \$1,300=\$1,300\times e^{0.074t}\\ \\ 0.074t=\ln 2\\ \\ t=\ln 2/0.074=9.37years](https://tex.z-dn.net/?f=2%5Ctimes%20%5C%241%2C300%3D%5C%241%2C300%5Ctimes%20e%5E%7B0.074t%7D%5C%5C%20%5C%5C%200.074t%3D%5Cln%202%5C%5C%20%5C%5C%20t%3D%5Cln%202%2F0.074%3D9.37years)
<u>2. For the amount to triple:</u>
<u />
![3\times \$1,300=\$1,300\times e^{0.074t}\\ \\ 0.074t=\ln 3\\ \\ t=\ln 3/0.074=14.85years](https://tex.z-dn.net/?f=3%5Ctimes%20%5C%241%2C300%3D%5C%241%2C300%5Ctimes%20e%5E%7B0.074t%7D%5C%5C%20%5C%5C%200.074t%3D%5Cln%203%5C%5C%20%5C%5C%20t%3D%5Cln%203%2F0.074%3D14.85years)
Answer:
Call for someone then you need to help them as much as you can
Answer:
The company should buy the units because it will save $10,000.-
Explanation:
Giving the following information:
Make in-house:
Unitary variable cost= 2 + 8 + 6= $16
Avoidable fixed cost= $8,000
Buy:
Unitary cost= $15
<u>First, we will determine the total cost of each option:</u>
Make in house= 2,000*16 + 8,000= $40,000
Buy= 15*2,000= $30,000
The company should buy the units because it will save $10,000.-
Answer:
n = ㏒ P ÷ ㏒ (1.08)
Explanation:
Compound interest rate
A = P × ![(1 + r)^{n}](https://tex.z-dn.net/?f=%281%20%2B%20r%29%5E%7Bn%7D)
where
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
A = amount of money accumulated after n years, including interest.
n = number of years
Since we want the principle amount to double i.e., A = 2P
put this in above equation
2P = P × ![(1 + r)^{n}](https://tex.z-dn.net/?f=%281%20%2B%20r%29%5E%7Bn%7D)
divide both sides by P, we get
P = ![(1 + r)^{n}](https://tex.z-dn.net/?f=%281%20%2B%20r%29%5E%7Bn%7D)
put r = 0.08
P = ![(1 + 0.08)^{n}](https://tex.z-dn.net/?f=%281%20%2B%200.08%29%5E%7Bn%7D)
P = ![(1 .08)^{n}](https://tex.z-dn.net/?f=%281%20.08%29%5E%7Bn%7D)
Taking log on both sides
㏒ P =㏒ ![(1 .08)^{n}](https://tex.z-dn.net/?f=%281%20.08%29%5E%7Bn%7D)
㏒ P = n ㏒ (1.08)
n = ㏒ P ÷ ㏒ (1.08)
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