Mathematics, 22.07.2019 22:00 spearjj

Solve this application using logarithms. at his son's birth, a man invested $2,000 in savings at 6% for his son's college education. approximately how much, to the nearest dollar, will be available in 19 years? ≈$ at his son's birth, a man invested $2,000 in a mutual fund earning 6.5% for his son's college education. approximately how much, to the nearest dollar, will be available in 19 years? real value ≈ $ for each of the man’s investments described above, how many years will it take for each investment to double in value? round your answers to the nearest whole year. years to double savings account years to double mutual fund

Answers: 1

Show answers

Answers

Part A:

Given that a man invested $2,000 in savings at 6%. In 19 years, the value of the investment will be:

$FV=2000(1+0.06)^{19} \\ \\ =2000(1.06)^{19}=2000(3.0256) \\ \\ \approx\$6,051$

Part B:

Given that a man invested $2,000 in a mutual fund earning 6.5%. In 19 years, the value of the investment will be:

$FV=2000(1+0.065)^{19} \\ \\ =2000(1.065)^{19}=2000(3.3086) \\ \\ \approx\$6,617$

Part C:

Given that a man invested $2,000 in savings at 6%. The number of years it will take for the value of the investment to double is obtained as follows:

Let the required number of years be n, then

$2000(1.06)^n=4000 \\ \\ \Rightarrow(1.06)^n=2 \\ \\ \Rightarrow n\log{(1.06)}=\log{2} \\ \\ \Rightarrow n= \frac{\log{2}}{\log{1.06}} = \frac{0.6931}{0.0583} =11.9\approx12$

Therefore, it will take the savings 12 years to double in value.

Part D:

Given that a man invested $2,000 in a mutual fund earning 6.5%. The number of years it will take for the value of the investment to double is obtained as follows:

Let the required number of years be n, then

$2000(1.065)^n=4000
 \\ \\ \Rightarrow(1.065)^n=2 \\ \\ \Rightarrow n\log{(1.065)}=\log{2} 
\\ \\ \Rightarrow n= \frac{\log{2}}{\log{1.065}} = \frac{0.6931}{0.0630}\approx11$

Therefore, it will take the investment 11 years to double in value.

Answer from: Quest

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the (original price) is $420.

0.7x = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

Answer from: Quest

true

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 12:50

What is the value of y in the solution to the system of equations? x + y = 12x – 3y = –30a. –8b. –3c. 3d. 8

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

You eat 8 strawberries and your friend eats 12 strawberries from a bowl. there are 20 strawberries left. which equation and solution give the original number of strawberries?

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

Quadrilateral ghjk has vertices g(2, 3), h(8, 2), j(6, 8), and k(3, 6). it is transformed according to the rule t(–4, –5). what are the coordinates of g”? (–7, 3) (–2, 2) (–1, –7) (2, –2)

Answers: 2

Answer

Mathematics, 21.06.2019 17:20

7. if the value of x varies directly with the value of y, and x = 3 when y = 21. what is the valu y, and x = 3 when y = 21. what is the value of x when y = 105?

Answers: 1

Answer

You know the right answer?

Solve this application using logarithms. at his son's birth, a man invested $2,000 in savings at 6%...

Questions

Mathematics, 27.08.2019 05:30

Find the error in the solution, and then solve it correctly. 7x + 12 + 6x = 1 7x + 12 = −5 7x = −17 x = −17 7...