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wlad13 [49]
3 years ago
7

7400 dollars is placed in an account with an annual interest

Mathematics
1 answer:
Anastasy [175]3 years ago
6 0

Answer:

17

Step-by-step explanation:

We have the following equation for compounding annual interest

AV=PV(1+i)ⁿ

We have

19200=7400(1+.06)ⁿ

Solve for n

divide both sides by 7400

2.594=(1.06)ⁿ

then use the following rule for exponents

x^y=z\\log_xz=y

which means that

log_{1.06}2.594=n

Solve and get

16.362

which rounds to 17

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Answer:

C. $118,000 and $110,000, respectively.

Step-by-step explanation:

Please consider the complete question.

An automobile firm wants to purchase either machine A or machine B. The intial cost of machines A and B are $40,000 and $50,000, respectively. The power consumption per year of machines A and B are 120 MWh and 100 MWh, respectively. The power cost is $40/MWh. The estimated operating and maintenance cost over 10 years is $30,000 for machine A and $20,000 for machine B.

First of all, we will find the amount spent on power consumption for 10 years by each machine as:

\text{Machine A}=10\cdot 120(\$40)\\\text{Machine A}=\$48,000

\text{Machine B}=10\cdot \$100(\$40)\\\text{Machine A}=\$40,000

Now, we will find overall cost of machines A and B by adding initial cost, power consumption for 10 years and maintenance cost as:

\text{Overall cost of machine A}=\$40,000+\$48,000+\$30,000

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\text{Overall cost of machine B}=\$50,000+\$40,000+\$20,000

\text{Overall cost of machine B}=\$110,000

Therefore, the overall cost of machines A and B are $118,000 and $110,000, respectively and option C is the correct choice.

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