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
Which of the following is most likely the result of religious socialization?
kumpel [21]
Believing in a spiritual higher being
4 0
3 years ago
Suppose xy=−4 and dy/dt=−3. Find dx/dt when x=−1.
user100 [1]
When x=-1: \quad (-1)y=-4\qquad\to\qquad y=4\)

Ok that gives us a little more information.
If we implicitly differentiate with respect to t, from the very start, then we can apply our product rule, ya?

x'y+xy'=0

The right side is zero, derivative of a constant is zero.
Where x' is dx/dt and y' is dy/dt.

From here, plug in all the stuff you know:
y' = -3
x = -1
y = 4

and solve for x'.

Hope that helps!
4 0
3 years ago
You are given 3 to 1 odds against tossing three tails with three​ coins, meaning you win ​$3 if you succeed and you lose ​$1 if
valentina_108 [34]

Step-by-step explanation:

  • To find the E(X) expected value, you come up with the different probabilities for each outcome
  • your set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tails
  • Each element has a probability of 1/8 so let x represent number of tails
  • Probability(x)=P(x)\\P(0)=\frac{1}{8} \\P(1)=\frac{3}{8} \\P(2)=\frac{3}{8} \\P(3)=\frac{1}{8}
  • The E(x)=Summation (x times P(x))
  • E(X)=(0)(0.125)+(1)(0.375)+(2)(0.375)+(3)(0.125)=1.5
  • Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tails
  • So you can expect to lose money in 1 game
  • But as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 games
8 0
3 years ago
Please help!!!!!!!!!!!!!!!
Nuetrik [128]

Answer:

5 and 7.

Step-by-step explanation:

Supplementary angles are angles that have a sum of 180°.

130° + 50° = 180°

120° + 60° = 180°

4 0
3 years ago
Which equation has infinitely many solutions?
Snezhnost [94]

Answer:

Bbbbbbbbbbbbbbbbbbbbbb

4 0
3 years ago
Other questions:
  • The sum of 14 and a number is equal to 17
    12·1 answer
  • How will you order from least to greatest the following numbers 0.5, 0.10, 0.18 and 0.75
    15·2 answers
  • What are the mean and the mode of the following set of data: 5, 12, 1, 5, 7
    10·2 answers
  • Suppose 8 out of every 20 students are absent from school less than five days a year.How many students would be absent from scho
    5·1 answer
  • If an ice cream store has 4 different flavors, Apple, Blueberry, Cantaloupe, and Duck.
    13·1 answer
  • Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.
    12·1 answer
  • What is the factored form of 25b^2-60b+36​
    12·2 answers
  • The probability that Brian buys a sandwich is 0.1. The probability that Brian gets the bus is 0.6. Assuming the events are indep
    15·2 answers
  • A vertical parabola goes through (1,-2), (-3, 10), and (4, 31). Use matrices to
    9·1 answer
  • Look at the picturee
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!