n- ? 1) When loan officers speak to people about taking out a loan for a certain principal, P at a certain monthly rate, they always have to balance two quantities, the monthly payment, m] with the number of payments, n] it takes to pay off the loan. These two vary inversely. All of these quantities can be related by the formula: Por 1-(1+r)¯" m= Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20-year period.. 110

Answers

Answer 1

[tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex] is the monthly payment

What is Compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

According to given question:

Principle Amount (P) = $200, 000

Rate(r) = 4% yearly

Rate(r) = 4/12 % Monthly

Rate(r) = 1/3 % Monthly

Time = 20 years = 240 months

⇒ 240 is the number of payment needed to pay

n = 240

Therefore, the monthly payment needed to pay

⇒ [tex]m = \frac{P.r}{1-(1-r)^{-n} }[/tex]

⇒ [tex]m = \frac{200000.1/3}{1-(1-1/3)^{-240} }[/tex]

⇒ [tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex]

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Related Questions

In a group of 500 people determine how many are suspects in the following scenario.

A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.

30 people total in the office

22 wearing a white button down shirts

16 wearing black pants

7 wearing a multicolored tie

Using the data, how many suspects are there?

Answers

Using the given data, the number of suspects is; 7

How to find the intersection of mathematical sets?

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects = A ∩ B ∩ C = 7 people

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