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Yanka [14]
3 years ago
11

1 point

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0

Answer:

last option

Step-by-step explanation:

y + 3 = 2 ( x - 1 )

⇒ y + 3 = 2x - 2

⇒ y = 2x - 5

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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
3 years ago
What is the slope of the line that is parallel to a line whose equeation is 3y = -4x + 2 ?
Novay_Z [31]
-----------------------
Find Slope :
-----------------------
3y = -4x + 2
y = -4/3x + 2/3

Slope = - 4/3

-----------------------
Answer: -4/3
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8 0
3 years ago
Read 2 more answers
What is the median of this set of measurements? 10cm, 15cm, 15cm, 18cm, 20cm.
Alinara [238K]

Answer:

15 cm

Step-by-step explanation:

Median means middle number

10,15,15,18,20

4 0
3 years ago
Read 2 more answers
Pls Help anyone. Ill will give brainliest and you will get 45 points pls anyone pls ㏒㏒㏒㏒㏒㏒
frosja888 [35]
The answer is E: (b-c)(a+c)
3 0
3 years ago
Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have t
zhannawk [14.2K]

Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive. He wants each bag to have the same amount of pasta and sauce and wants to use all of the items. Use the drop-down menus to complete the statements below about the number of bags Cesar can make.

What is the greatest number of bags Cesar can make and Each bag would have _____ pasta and _____ jars of sauce

Answer:

The greatest number of bags Cesar can make is 16 bags.

Each bag would have 2 pasta and 3 of jars of sauce

Step-by-step explanation:

We solve the above question using Greatest Common Factor method

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then the greatest common factor is 16.

Hence, the greatest number of bags Cesar can make is 16 bags.

For Pasta, We have 32 pasta

Each bag would have: 32/16

= 2 pasta

For Jars of sauce, we have 48 jars of sauce.= 48/16

= 3 jars of sauce

4 0
3 years ago
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