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2 years ago

Rita drank the following ounces of milk during the last week

Mathematics

1 answer:

Andre45 [30]2 years ago

3 0

Answer:

Mean = 14.14

Mode = 14

Median = 14

Range = 16

Step-by-step explanation:

Given Data Set : 18 , 14 , 10 , 22, 14 , 15 and 6

Identifying the mean

Mean = Sum of given data values / total # of given values

Here sum of given data values = 18 + 14 + 10 + 22 + 14 + 15 + 6 = 99

And there are 7 given data values

So mean = 99 / 7 =

14.14

( approximately )

Identifying the mode

The mode is the number that appears most often

14 appears twice, which is the most times out of any other value

Hence, the mode is

Identifying the median

The median is the middle number in terms of value

To make this easier, its best to order the given values from least to greatest
Doing so we acquire 6 , 10 , 14 , 14 , 15 , 18 , 22

Then you go to the middle of the listed terms.

Doing so we would end up with 14 being in the middle

Hence the median is

Identifying the range

Range = largest given value - smallest given value

Here the most rita drank was 22 ounces and the least amount of milk she drank was 6 ounces

So the range would be 22 - 6 =

ounces

And we are done!

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The time value of money calculation can be performed using formula equations or online calculators.

The correct responses are;

1) Option 3

2) Option 2

3) The difference in principal is approximately $8,000

The difference in interest earned is approximately $2,977.87

4) It is better to invest more money at the beginning of the 30 years

Reasons:

Option 1: Present value = 0

Amount invested per month, A = $25/month

The Annual Percentage Rate, APR, r = 3.25%

Number of years = 30

The future value of an annuity is given by the formula;

$\displaystyle FV_{A} = \mathbf{A \cdot \left (\frac{ \left(1 + \frac{r}{m} \right)^{m\cdot t} - 1}{\frac{r}{m} } \right)}$

In option 1, m = 12 periods per year

Therefore;

$\displaystyle FV_{A} = 25 \times \left (\frac{ \left(1 + \frac{0.0325}{12} \right)^{12 \times 30} - 1}{\frac{0.0325}{12} } \right) \approx \mathbf{15,209.3}$

Contribution = $25 × 12 × 30 = $9,000

Total interest earned = $15,209.3 - $9,000 = $6,209.3

Final balance = $15,209.3

Option 2: Present value = 0

Amount, A = $75/quarter

m = 4 periods per year

The Annual Percentage Rate, APR = 4.00%

Therefore;

The effective interest rate is therefore;

$\displaystyle r_{eff} = \left(1 + \frac{0.04}{4} \right)^4 - 1 \approx \mathbf{0.04060401}$

$\displaystyle FV_{A} = 75 \times \left (\frac{ \left(1 + \frac{0.04060401}{4} \right)^{4 \times 30} - 1}{\frac{0.04060401}{4} } \right) \approx 17,437.7$

Using an online calculator, FV = $17,467.04

Contribution = $75 × 4 × 30 = $9,000

Total interest earned = $17,467.04 - $9,000 = $8,467.04

Final balance = $17,467.04

Option 3: Present value = $1,000

APR = 6.25%

m = 12 period per year

Number of years, t = 30 years

Therefore;

$\displaystyle FV = \left (1 + \frac{0.0625}{12} \right)^{12 \times 30} \approx \mathbf{6,489.17}$

Contribution = $1,000

Total interest earned = $6,489.17 - $1,000 = $5,489.17

Final balance = $6,489.17

The table of values is therefore;

$\begin{tabular}{|c|c|c|c|}Option \# &Contribution &Total Interest Earned&Final Balance\\1&\$9,000&\$6,209.3 & \$15,209.3\\2&\$9,000&\$8,467.04 &\$17,467.04\\3&\$1,000&\$5,489.17&\$6,489.17\end{array}\right]$

1) The option that has the least amount invested are option 3

Option 3 investment plan is a present value of $1,000, invested for 30 years at 6.25% APR compounded monthly.

2) Option 2 yielded the highest amount at the end of 30 years, given that the APR is higher than the APR for option 1, although the amount invested over the period are the same.

The basis of option 2 investment plan is $75 invested quarterly at 4.00% APR compounded monthly for 30 years.

3) The difference in the principal invested for the highest and lowest final balance is $9,000 - $1,000 = $8,000

The difference in the interest earned is; $8,467.04 - $5,489.17 = $2,977.87

4) In option 1 the present value is zero, therefore zero amount was invested at the beginning.

The interest to investment ration is 6,209.3:9,000 ≈ 0.7:1

In option 3, all the money was invested at the beginning.

The interest to investment ratio of option 3 is; 5,489.17:1,000 ≈ 5.5:1

Given that the interest to investment ratio, which is the return on investment is larger when more money is saved at the beginning as in option 3, it is better to invest more money at the beginning.

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