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blsea [12.9K]
3 years ago
6

What is the LCM of 30 and 45? a0

Mathematics
2 answers:
Alik [6]3 years ago
8 0
90 is the LCM of 30 and 45
Bess [88]3 years ago
3 0
30, 60, 90
45, 90

LCM equals 90
You might be interested in
How Much Have I Saved? Portfolio
avanturin [10]

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 <u>option 3</u>

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

2) <u>Option 2</u> 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 = <u>$8,000</u>

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

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, <u>it is better to invest more money at the beginning</u>.

Learn more about future value of an annuity here:

brainly.com/question/8243704

3 0
2 years ago
Can someone help me find the diameter? <br><br> also what is a diameter even?
lukranit [14]

Answer:

24

Step-by-step explanation:

area of circle = πr²

πr² = 144π

Cancel out π

r² = 144

r = √144

r = 12

diameter = 2 x radius

diameter = 2 x 12

diameter = 24m

* diameter is the "width of a circle", the distance from the widest points of the circle

3 0
2 years ago
Simplify help me plss cuz I don’t find the answer
dusya [7]
32^(-1/5)

1/32^(1/5)

^1/5 means 5√32 = 2

so the answer is 1/2 or 0.5
6 0
3 years ago
In the Itty Bitty High School, there are 85 students. There are 27 students who take French, 51 who take Geometry and 38 who tak
andrew-mc [135]

Answer:

58 students

Step-by-step explanation:

Given

Total = 85

French = 27

Geometry = 51

History = 38

None = 5

All = 2

Required

Students that take only 1 subjects

The attached image illustrates the question.

For French only (x), we have:

x + 7 -2+10-2+2=27

x + 15=27

Collect like terms

x =- 15+27

x =12

For Geometry only (y), we have:

y+10-2+15-2+2=51

y+23=51

Collect like terms

y=-23+51

y=28

For History only (z), we have:

z +15-2+7-2+2=38

z +20=38

Collect like terms

z =-20+38

z =18

Students with one subject is then calculated as:

1\ subject = x+y+z

1\ subject = 12 + 28 + 18

1\ subject = 58

5 0
2 years ago
11y - |x|; if x = -10 and y = 2
bonufazy [111]

Answer:

- 8

Step-by-step explanation:

x = - 10

y = 2

I x I

= I - 10 I

= 10

y - I x I

= 2 - 10

= - 8

7 0
3 years ago
Read 2 more answers
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