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tester [92]
3 years ago
8

your family leaves your town traveling at an average rate of 45 mi/h two hours later, your neighbor leaves town traveling along

the same road at an average rate of 60 mi/h how many hours will it take your neighbor to overtake you
Mathematics
1 answer:
vladimir2022 [97]3 years ago
8 0
To find the answer to this question, we first need to know how many miles the family has gone. We can do this using the formula D = R * T

D = 45 * 2
D = 90

Now we know how many miles the family is in front of the neighbor before he starts driving. Now we need to find how much faster the speed of the neighbor is compared to the family. 

60 - 45 = 15, so the neighbor goes 15 mph faster. To find how long it will take for the neighbor to overtake the family, we need to calculate the time it will take for the neighbor to catch up 90 miles. We can do this by dividing 90 by 15 (because that's how much faster the neighbor is).

90/15 is 6, so it will take the neighbor 6 hours to overtake the family. 
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Answer:

Part A: The value of the simple interest investment at the end of three years is $12,220

Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C: The simple interest investment is better over the first three years

Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Step-by-step explanation:

Part A:

A = P + P r t, where

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∵ First option offers 7.4% per year simple interest

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∵ He may not withdraw any of  the money for three years after

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∴ t = 3

- Substitute all of these values in the formula above

∴ A = 10,000 + 10,000(0.074)(3)

∴ A = 10,000 + 2,220

∴ A = 12,220

The value of the simple interest investment at the end of three years is $12,220

Part B:

A=P(1+\frac{r}{n})^{nt}, where

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∵ George deposits $10,000

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∵ The second option offers a 6.5% interest rate compounded quarterly

∴ r = 6.5% = 6.5 ÷ 100 = 0.065

∴ n = 4 ⇒ quarterly

∵ He may not withdraw any of  the money for three years after

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∴ t = 3

- Substitute all of these values in the formula above

∴ A=10,000(1+\frac{0.065}{4})^{(4)(3)}

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∴ A = 12,134.08

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∵ 12,220 > 12,134.08

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I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

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