1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Cloud [144]
3 years ago
15

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

y one month from today. The interest being charged on this loan is constant (but unknown).
For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage:

(b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $25044.84
Mathematics
1 answer:
Makovka662 [10]3 years ago
7 0

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%.

You might be interested in
Slove for x, please. ​
KATRIN_1 [288]

Answer:

I do not know

Step-by-step explanation:

6 0
3 years ago
What number should be added to both sides of the following equation to solve for x?
son4ous [18]

Answer:

7 is your answer

Step-by-step explanation:

Hope that helps you

5 0
3 years ago
Read 2 more answers
a 6ft tall man casts a shadow that is 9ft long. at the same time, a tree nearby casts a 48 ft shadow. how tall is the tree
Jlenok [28]
The tree is 45ft tall
5 0
3 years ago
Read 2 more answers
A survey showed that 77​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 22 adults are
Sveta_85 [38]

Answer:

The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .

Step-by-step explanation:

A survey showed that 77​% of adults need correction for their eyesight.

If 22 adults are randomly​ selected, find the probability that no more than more than 11 of them need correction for their eyesight.

n =22

p = 0.77

q = 1-p = 1- 0.77=0.23

We are supposed to find P(x\leq 11)

P(x\leq 11)=P(x=1)+P(x=2)+P(x=3)+.....+P(x=11)

Formula : P(x=r)=^nC_r p^r q^{n-r}

P(x\leq 11)=^{22}C_1 (0.77)^1 (0.23)^{22-1}+^{22}C_2 (0.77)^2 (0.23)^{22-2}+^{22}C_3 (0.77)^1 (0.23)^{22-3}+.....+^{22}C_{11} (0.77)^1 (0.23)^{22-11}

Using calculator

P(x\leq 11)=0.00512

So, The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .

3 0
3 years ago
If it takes John 15 minutes to run 2 miles, how long will it take to run a 6 mile race at this same pace?
Maksim231197 [3]

Answer:

45

Step-by-step explanation:

15 x 3 is 45

7 0
2 years ago
Read 2 more answers
Other questions:
  • 11x - 3 + 4x greater than or equal to 142 1/2
    7·1 answer
  • the leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the tri
    6·1 answer
  • Write an equation for the n th term of the arthemeric sequence 6,3,0,-3
    5·1 answer
  • You purchase a $220 airline ticket. you have a discount code to recieve 10% off. There is 10.5% service charge added to the tota
    11·2 answers
  • A sports fan conducted a test to investigate whether male high school athletes are
    6·1 answer
  • Multiply.<br> 35<br> 22<br> x____
    14·2 answers
  • How many terms are in the following expression?<br><br> 2x + 8 - 3y<br><br> PLEASE HELP ASAP!
    15·1 answer
  • Find the slope of the line through each pair of points.<br> (2,-2),(4,2)
    13·1 answer
  • What is the slope of the line y=1/6x+3/2
    9·1 answer
  • On a horizontal number line, numbers are what
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!