40% of what number is 14

A loan of $100,000 is made today. The borrower will make equal repayments of $3568 per month with the first payment being exactl

Makovka662 [10]

Answer:

The yearly interest rate is 5.20%.

Step-by-step explanation:

This is a compound interest problem

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

The loan outstanding is the value of the loan that has not been repaid.

Here, it is $$25,044.84$ .

To find the interest rate, we first have to find how much money the borrower will have to pay, that will be the value of A in the compound interest formula.

The total he will have to play is $$25,044.84$ plus the $3,568 he has already paid in each of the previous 2 years = 24 months. So:

$A = 25,044.84 + 24*3,568 = 110,676.84$ .

P is the value of loan, so $P = 100,000$

r is the interest rate, the value we have to find.

We have to find the annual interest rate, so $n = 1$ .

We found the total amount in 2 years, so $t = 2$ .

Solving

$A = P(1 + \frac{r}{n})^{nt}$

$110,676.84 = 100,000(1 + r)^{2}$

$(1 + r)^{2} = 1.1067684$

To find r, i will take the square root of both sides of the equation. So

$\sqrt{(1 + r)^{2}} = \sqrt{1.1067684}$

$1 + r = 1.0520$

$r = 0.0520$

The yearly interest rate is 5.20%.

7 0

3 years ago

In a linear equation relating income and consumption, you know that the intercept is $1,000 and the slope of the line is 4. if i

Amiraneli [1.4K]

A general equation of a linear function is expressed as y = mx + b where m represents the slope and b is the y-intercept. The slope is the rate of change of y with respect x which is equal to 4 for this problem. The y-intercept represents the value when x is equal to zero. It is the initial value of y. In this case, it is equal to $1,000. The linear equation would be:

y = 4x + 1000

assuming y is the income and x is the consumption.

At an income (y) equal to $20,000, we can calculate for the consumption.

20000 = 4x + 1000
19000 = 4x
x = 4750

3 0

3 years ago

Determine if x=2 is a solution.

Marrrta [24]

Answer:

Do you have a picture for the problem that you want to be solved?

3 0

3 years ago

Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuo

Sliva [168]

a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is <u>$11,949.50</u>.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

<h3>How is the future value determined?</h3>

The future value can be determined using an online finance calculator.

Data and Calculations:

<h3>a) Compounded Semiannually:</h3>

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

<u>Result</u>:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

<h3>b) Compounded Continuously:</h3>

Using the formula A = Pert

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years): 8 years

<u>Result</u>:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is <u>$11,949.50</u>, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

Learn more about compounding interest at brainly.com/question/24274034

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8 0

2 years ago

What is 20/36 reduced

likoan [24]

20/36 reduced is 5/9. hope this helped! :)

7 0

3 years ago

Read 2 more answers