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an amount of money is invested at 3% annual simple interest, & $2000 more than that amount is invested at 4%. The total annual interest is $920. How much is invested at each rate?

Answers

Answer 1

Answer:

$12,000 at 3%.

$14,000 at 4%.

Explanation:

Let A be the amount invested at 3%, and B be the amount invested at 4%. The following system of equations can be modeled from the provided information:

[tex]B=A+2,000\\0.03A+0.04B = 920\\[/tex]

Solving the linear system:

[tex]B=-0.75A+23,000\\-0.75A+23,000 = A+2,000\\A= 12,000\\B=14,000[/tex]

$12,000 were invested at 3% and $14,000 were invested at 4%.

Related Questions

Mr. James purchased a vacation house in Los Angeles on July 1, 2017. The purchase price was $1,000,000, and Mr. James spent $10,000 on capital additions. As of January 1, 2019, the house was worth $1,200,000. Mr. James was not entitled to depreciate thehouse as it was a personal-use asset.Assume Mr. James still owned the house as of December 31, 2019. On December 31,2019, the house was valued at $1,300,000. For tax purposes, how much income did Mr.James realize in 2019

Answers

Answer:

= $210,000

Explanation:

The question is to determine the income realized by Mr. James in 2019

The income is calculated as follows:

First, the basic information for calculation:

The Purchase price for the vacation house = $1,000,000

Spent Capital additions = $10,000

2019 worth of the house = $1,200,000

Secondly, based on the extracted figures, the income is calculated  as follows

Income realised in 2019 = 2019 worth of the house - (Purchase Price - capital addition)

= $1,200,000 - ($1,000,000 - $10,000)

= $1,200,000 - $990,000

= $210,000

Final answer:

Mr. James did not realize any income from the increase in value of his house in 2019 for tax purposes as the house was not sold.

Explanation:

For tax purposes, income is normally the amount of money received for goods or services during a certain time period. However, any increase in the value of personal assets such as a house, also known as appreciation, is not counted as income until the asset is sold. So, in 2019, even though the value of Mr. James' house increased by $100,000, from $1,200,000 on January 1 to $1,300,000 on December 31, 2019, Mr. James would not have realized, or officially 'made,' any income from his home in 2019 unless he sold it. Therefore, for tax purposes, the answer is $0.

Learn more about Income Realization here:

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