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Fudgin [204]
3 years ago
8

Gabe and Eugenia bought a house! Their loan is for $117,000 , for 15 years at an annual interest rate of 4% . This results in a

monthly payment of $865.43 . If only the minimum payment is made in month one, how much of the first payment goes toward reducing her balance? First, let's find the amount of interest she paid in month 1
Mathematics
1 answer:
cupoosta [38]3 years ago
4 0

Answer:

Principal element is $475.43

Interest payment is $390

Step-by-step explanation:

The amount of interest paid in month one is 4%*$117,000*1/12=$390

The interest is calculated based on the annual interest rate of 4% apportioned to reflect one month interest by multiplying by 1/12

The principal element of monthly payment is the monthly payment minus interest.

principal paid in month one=$865.43-$390=$475.43

Ultimately,$475.43 goes toward reducing her loan balance while the $390 is interest on loan

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Answer:Answer:

\sum\left {{7} \atop {1}} \right -n(3+n)

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as S_n = \frac{n}{2}[2a+(n-1)d]

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Required

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S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 =  \frac{7}{2}[-8+(6)(-2)]\\\\S_7 =  \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70

The sum of the nth term of the sequence will be;

S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n =  \frac{-6n}{2} -  \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)

The sigma notation will be expressed as \sum\left {{7} \atop {1}} \right -n(3+n). <em>The limit ranges from 1 to 7 since we are to  find  the sum of the first seven terms of the series.</em>

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Answer:

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