Mathematics, 11.10.2019 00:00 jam3381

Will is 30 years old and works for a company that matches his 401(k) contribution up to 3%. the interest rate for his 401(k) is 7.13%. if he puts away 9% of his $41,000 salary every year, how much would he have saved in 10 years? round your answer to the nearest cent.
a.
$52,835.72
b.
$56,602.91
c.
$68,395.76
d.
$73,272.37

Answers: 1

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Answer from: avery58

Option (C) is correct.

Will has saved $68,395.76 in 10 years.

Step-by-step explanation:

Will puts 9% of his $41,000 salary every year

Therefore, $41000\cdot \frac{9}{100}=3690$

The employer contributes a maximum of 3% of the employee contribution, that is $41000\cdot \frac{3}{100}=1230$

Therefore, Total annual contribution of Will is ( 3690 + 1230) = $4920

After 10 years, total money Will saved is calculated as ,

$FV=\frac{P\left(\left(1+r\right)^n-1\right)}{r}$

Substitute n = 10

P = annual payment = $4920

r = rate of interest = 0.0713

We get,

$FV=\left(4920\right)\cdot\frac{\left(\left(1+0.0713\right)^{10}-1\right)}{0.0713}\\\\\ FV=68395.76$

Option (C) is correct.

Thus, Will has saved $68,395.76 in 10 years.

Answer from: lilzaya510

c. $68,395.76

Step by step explanation:

We have been given that Bill contributes 9% of his $41,000 salary every year for his 401(k). The company matches his 401(k) contribution up to 3%.

First of all let us find 12% (9%+3%) of $41,000.

$\text{Amount contributed to Will''s 401(k) annually}=\frac{12}{100}\times \$41,000$

$\text{Amount contributed to Will''s 401(k) annually}=0.12\times \$41,000$

$\text{Amount contributed to Will''s 401(k) annually}=\$4920$

Therefore, $4920 is contributed to Will's 401(k) annually.

Now we will use regular deposits formula to find the amount of money saved in 10 years.

$P=M((1+\frac{i}{q})^{nq}-1)*(\frac{q}{i})$ , where,

= Amount after n years,

= Deposit amount per period,

= Interest rate in decimal form,

= Number of deposits in a year,

= Number of years.

Let us convert our given interest rate in decimal form.

$7.13\%=\frac{7.13}{100}=0.0713$

Upon substituting our given values in regular deposit formula we will get,

$P=4920((1+\frac{0.0713}{1})^{10*1}-1)*(\frac{1}{0.0713})$

$P=4920((1+0.0713)^{10}-1)*(\frac{1}{0.0713})$

$P=4920((1.0713)^{10}-1)*(\frac{1}{0.0713})$

P=4920(1.9911824193596552-1)*(14.0252454417952314)

P=4920(0.9911824193596552)*(14.0252454417952314)

P=4920*13.9015767091

$P=68395.7574088289\approx 68395.76$

Therefore, Will would have saved $68395.76 in 10 years and option c is the correct choice.

Answer from: Quest

send it over

step-by-step explanation:

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

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