a $1600 principal earns 7% annual interest, compounded semiannually. What is the balance after 33 years?

Answer:

the final answer is the last option, D

Step-by-step explanation:

Answer:

  D.  $877.96

Step-by-step explanation:

You want the amount saved if a 20 year loan of $60,000 at 4.4% is paid off 3 years early.

The monthly payment on the loan can be found from ...

  [tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-12t})}[/tex]

where P is the loan amount at rate r for t years.

For the 20 year loan of $60,000 at 4.4%, the payment is calculated as ...

  [tex]A=\dfrac{60000(.044)}{12(1-(1+0.044/12)^{-12\cdot20})}=\dfrac{220}{0.584549}=376.3585[/tex]

After 204 payments on the loan, the remaining balance due is ...

  [tex]A=P\left(1-\dfrac{(1+r/12)^n-1}{(1+r/12)^{12t}-1}\right)\\\\\\A=60000\left(1-\dfrac{1.0036667^{204}-1}{1.0036667^{240}-1}\right)=12671.04[/tex]

The remaining 36 payments on the loan come to about ...

  36 × 376.3585 ≈ 13548.91

So, the savings from early payoff is about ...

  13548.91 -12671.04 ≈ 877.86

Choice D, $877.96, is the best match for this value.

__

Additional comment

The actual savings will depend on the details of rounding of intermediate values in the calculation, and on the timing of the early payment. If the loan is amortized over 17 years, so more is paid each month, the savings can be more than $5000.

Here, we have calculated the savings on the assumption that payment number 204 includes the payoff amount.

Using the loan formula, monthly payments are $458.14. Remaining balance after 17 years is approximately $58,214.19. The savings would be approximately $1,785.81. The closest option to this calculation is  C. $376.36

To calculate the amount saved by paying off the loan 3 years early, we need to find out the remaining balance of the loan after 17 years (20 years - 3 years). Then, we compare the remaining balance to the original balance to find the savings.

Let's break down the steps:

1. Find the monthly interest rate (r):

[tex]\[ r = \frac{4.4\%}{12} = \frac{0.044}{12} \][/tex]

2. Calculate the total number of payments (n):

[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]

3. Use the formula for the monthly payment (PMT) of a loan:

[tex]\[ PMT = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \][/tex]

where:

P = principal amount (loan amount)

r = monthly interest rate

n = total number of payments

We'll use PMT to find out the monthly payment Arthur has to make.

4. Use the monthly payment (PMT) to find the remaining balance after 17 years (204 months).

5. Finally, calculate the savings by comparing the remaining balance to the original loan amount.

Let's do the calculations:

1. Monthly interest rate:

[tex]\[ r = \frac{0.044}{12} = 0.00367 \][/tex]

2. Total number of payments:

[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]

3. Monthly payment (PMT):

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1 + 0.00367)^{240}}{(1 + 0.00367)^{240} - 1} \][/tex]

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1.00367)^{240}}{(1.00367)^{240} - 1} \][/tex]

[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot 1.937}{1.937 - 1} \][/tex]

[tex]\[ PMT = \frac{429.33}{0.937} \][/tex]

[tex]\[ PMT= 458.14 \][/tex]

4. Remaining balance after 17 years (204 months):

[tex]\[ PV = \frac{PMT \cdot (1 - (1 + r)^{-n})}{r} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot (1 - (1 + 0.00367)^{-204})}{0.00367} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot (1 - 0.533)}{0.00367} \][/tex]

[tex]\[ PV = \frac{458.14 \cdot 0.467}{0.00367} \][/tex]

[tex]\[ PV = \frac{213.94}{0.00367} \][/tex]

[tex]\[ PV = 58214.19 \][/tex]

5. Savings:

Savings = 60000 - 58214.19

Savings ≈ 1785.81

So, Arthur would save approximately $1785.81 by paying off the loan 3 years early.

The closest option to this calculation is  C. $376.36

Based on the right-angled triangle, the value of m is equal to: C. [tex]\sqrt{95}[/tex].

According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg.

Mathematically, the geometric mean (leg) theorem can be modeled by the following formula;

Hypotenuse/leg = leg/part

where;

hypotenuse = 14 + 5 = 19

leg = m

part = 5

By applying geometric mean (leg) theorem, the length of the part (x) can be calculated as follows;

19/m = m/5

By cross-multiplying, we have the following:

[tex]m^2=19 \times 5\\\\m^2=95\\\\m=\sqrt{95}[/tex]

Read more on geometric mean here: brainly.com/question/26257841

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For 52/9 to be expressed as a decimal, you need to divide the fraction.

52/9 = 5.78 (rounded by the 1hundreds in the decimals place).

Team A won 3g - 7 games, where g is the number of games won by Team C. To determine the number of games Team A won, multiply the number of games Team C won by 3 and subtract 7.

Let's denote Team C's number of wins as g. According to the information provided, Team B won three times as many games as Team C, which can be expressed as 3g. It is also stated that Team A won 7 fewer games than Team B. So, if Team B won 3g games, then Team A won 3g - 7 games.

To find the number of games Team A won, simply multiply the number of games Team C won by 3 and subtract 7 from that total. This can be represented by the algebraic expression A = 3g - 7, where A represents the number of games won by Team A and g represents the number of games won by Team C.

Answer:

  11 cm by 15 cm

Step-by-step explanation:

The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.

  165 = 1·165 = 3·55 = 5·33 = 11·15

The numbers in the last factor pair total 26. These are the dimensions.

The dimensions are 11 cm by 15 cm.

Normal Distributions

I couldn't see the whole graph in the answer above, but using the quartiles, I chose graph A and that was right.

1. b. mean=75.8, median=76.5, mode=63

2. a. dots at 50, 53.5, 58, 62.5, and 67

3. c. 30th percentile=105, 90th percentile=176.

This is a controversial question because some of the numbers repeat, but as of 5/19, answer c is right.

4. d. mean=8, variance=18.3, standard deviation=4.3

5. a. 2

6. b. 22%

7. d. a^6-30d^5+375d^4-2,500d^3+9,375d^2-18,750d+15,625

8. a. 93%

9. b. 16%

10. c. 84%

Using a system of equations, it is found that Tripp weighs 42 pounds and Rico weighs 7 pounds.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Tripp weighs exactly 35 pounds more than Rico, hence:

x = 35 + y.

Together, they weigh exactly 49 pounds, hence:

x + y = 49

35 + y + y = 49

2y = 14 -> y = 7

x = 35 + y -> x = 42

Hence, Tripp weighs 42 pounds and Rico weighs 7 pounds.

To learn more about a system of equations, you can check https://brainly.com/question/24342899

Answer:

Your answer would be a. or the first problem.

Step-by-step explanation: