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Gennadij [26K]
3 years ago
15

If m1= m_2, then m 21 is​

Mathematics
1 answer:
alexgriva [62]3 years ago
8 0

Answer:

45

Step-by-step explanation:

Angle 1 and angle 2 make 90 degrees and line C cuts through that so and they are equal so that makes 45 for the two of them and added together, it will equal 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
3 years ago
A penny is 0.061 inchthick. wath is the valuee of the 6 in the thickness of a penny
qaws [65]
The value of 6 is 6 hundreths
5 0
3 years ago
What’s equivalent (2x^5)^3
Over [174]

Answer:

8x^15

Step-by-step explanation:

(2x5)3

=(2x5)3

=2x5*2x5*2x5

=8x15

6 0
3 years ago
Laura and Martin obtain a 30-year, $180,000 conventional mortgage at 10.0% on a house selling for $210,000. Their monthly mortga
Westkost [7]

Answer:

total payment = $563,760

Interest = $383,760

Principal part = $66

Step-by-step explanation:

(a) total payment:

n = 30 years = 360 months

monthly payment = $1,566

Total payment = $1,566 * 360 months = $563,760

(b) interest:

Total payment = $563,760

Principal = $180,000

Total payment = Principal + Interest

Interest = Total payment - Principal

Interest = $563,760 - $180,000 = $383,760

(c) part of first payment applied to the principal:

First payment = $1,566

Principal = $180,000

Interest rate = 10% yearly = 10% / 12 = 0.8333% = 0.008333 monthly

Monthly interest = Principal * Interest rate = $180,000 * 0.008333 = $1,500

Principal part = $1,566 - $1,500 = $66

Hope this helps!

4 0
3 years ago
What’s the answer please i don’t need work shown :)
Lady bird [3.3K]

Answer:

102

You didn't ask for work and I shall respect your wish

6 0
2 years ago
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