Simplify the function f

Madeline received $300 for her birthday. She deposits it into a savings account with an interest rate of 2.45%. She makes monthl

oee [108]

Answer:

b. $1,587.57

Step-by-step explanation:

A financial calculator will tell you the value of Madeline's account after 8 years will be $16,287.57. In that time, she will have deposited ...

$300 +96×150 = $14,700

The interest earned is the difference between her account balance and the amount she deposited:

$16,287.57 -14,700 = $1,587.57 . . . interest earned

_____

<em>Account value calculation</em>

The future value of the initial $300 deposit after 8 years is ...

A = P(1 +r/n)^(nt)

for principal P earning annual rate r compounded n times per year for t years.

A = $300(1 +0.0245/12)^(12·8) ≈ $364.89

The future value of the sum of $150 deposits monthly (at the beginning of the month) will be ...

A = $150((1+r/n)^(nt) -1)(1 +n/r) = $15,922.68

So, the total value of Madeline's account in 8 years is ...

$364.89 +15,922.68 = $16,287.57

_____

<em>Comment on account value</em>

In problems of this nature, it is always necessary to determine when the deposits are made relative to when the account value is measured. Here, we assume the $300 deposit is immediate, and its value is measured 8 years hence.

The monthly deposits are not described in that detail. In order to get any of the numbers in the answer list, we need to assume the deposits are at the beginning of the month. If we assume they are at the end of the month, the amount of interest is reduced by about $33.18, the last month's interest.

7 0

3 years ago

The Johnson twins were born nine years after their older sister. This year, the product of the three siblings ages is exactly 18

KATRIN_1 [288]

Answer: The age of the twins is 10 years.

Step-by-step explanation:

Suppose the age of older sister be x

Let the age of twins sister be x-9, as they are born after 9 years.

Product of their ages be

$x(x-9)(x-9)\\\\=x(x^2-18x+81)\\\\=x^3-18x^2+81x$

Sum of their ages will be

$x+x-9+x-9\\\\=3x-18$

According to question,

$1861+3x-18=x^3-18x^2+81x\\\\x^3-18x^2+81x-3x+18-1861=0\\\\x^3-18x^2+78x-1843=0\\\\x=19$

So, Age of older sister will be 19 years.

Age of the twins will be

$19-9=10\ years$

Hence, the age of the twins is 10 years.

3 0

4 years ago

4 bells toll together at 9 am. They toll after 7, 8. 11 and 12 seconds respectively. How many times will they toll together agai

Svetach [21]

Answer:

5 times

Step-by-step explanation:

What we need to do here is to find the lowest common multiple of 7,8,11 and 12

This is;

1848

Now, let’s calculate the number of seconds in 3 hours

In 1 hour, we have 3600 seconds

In 3 hours, this will be;

3600 * 3 = 10,800 seconds

So, to find the number of times in which all 4 will toll together, we need to know the number of 1848 seconds in 10,800 seconds

Mathematically, that will be;

10,800/1848 = 5.844

Our answer will be 5 times however

This is because the sixth time they would have sounded together would be more than the 3 hours time frame

8 0

3 years ago

A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement. a) What is th

Kay [80]

Answer:

3.5

Step-by-step explanation:

you want to add all of the balls together and then divide by 4 because that's how many color balls there are

7 0

4 years ago

Of the population of all fruit flies we wish to give a 90% confidence interval for the fraction which possess a gene which gives

maks197457 [2]

Answer:

The margin of error for the 90% confidence interval is of 0.038.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.