Solving a Math Problem on Income with 5% Increases over 25 Years

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In summary, every year your income increases by 5%. After 24 years, your initial 5000 will have increased by 1.0524 times.
  • #1
darkmagic
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How do you solve this?
There is this kind of question in our test and I don't know how will I do it.

You're working in a company. Your starting income is 5000. Every year, the income will increase by 5%. What is your total income on your 25th year in the company?
 
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  • #2
This is a question, not a tutorial so I am moving out of "Learning Materials" to "Precalculus Homework and School Work".

You startwith income at 5000 and it increases by 5% each year.

Okay, the first year your increases by "5% of 5000"= .05(5000)= 250 so your income the second year is 5250= 5000+ (.05)5000= (1.05)(5000). At the end of that year it increases by "5% of 5250"= .05(5250)= 262.50 and the third year your income is 5512.50= 5250+ (.05)5250= (1.05)(5250)= 1.05(1.05(5000)). The reason I wrote it out like that is because neither you nor I want to do that 24 times! (During your 25th year, your income will have increased 24 times.) You should be able to see what is happening: each year your income is multiplied by 1.05. After 24 years, that initial 5000 is multiplied by 1.05 24 times: [itex](1.05)^{24}(5000)[/itex].
 
  • #3
[tex]a_1=5000[/tex]

[tex]a_2=a_1+a_1*\frac{5}{100}=a_1*1.05[/tex]

[tex]a_3=a_1*1.05 + a_1*1.05*0.05=a_1*1.05(1 + 0.05)=a_1*1.05*1.05[/tex]

[tex]a_4=a_1*1.05*1.05*1.05[/tex]

[tex].......[/tex]

[tex]a_{n+1}=a_1*(1.05)^{n}[/tex]

So a25=5000*(1.05)24

Regards.
 
Last edited:
  • #4
Is 1.05 constant?
 
  • #5
darkmagic said:
Is 1.05 constant?

Yep, its a constant.
 
  • #6
It's certainly not going to change!
 
  • #7
ok. where is that 1.05 come from?
 
  • #8
darkmagic said:
ok. where is that 1.05 come from?

If you see my way of solving the problem, you'll spot that

[tex]a_2=a_1+a_1*\frac{5}{100}=a_1(1+\frac{5}{100})=a_1\frac{100+5}{100}=a_1\frac{105}{100}=a_1*1.05[/tex]

See now where it comes from?
 
  • #9
darkmagic said:
ok. where is that 1.05 come from?
I thought I had said that. Each year, your income is the same as the previous year (100%) and an additional 5% raise. Together that means your income each year is 105% of the previous year's. 105% is the same as 1.05.
 
  • #10
If it helps anyone, you can work this sort of thing out on Calcatraz, my new online calculator.

Just enter it as: http://www.calcatraz.com/calc?c=%245000+raised+by+5%25+in+year+25" [Broken], substituting your own values.
 
Last edited by a moderator:

1. What is the formula for calculating income?

The formula for calculating income is total revenue - total expenses. This provides the net income or profit for an individual or company.

2. How do you calculate gross income?

Gross income is calculated by adding all sources of income, such as wages, tips, bonuses, and interest, before any deductions are made.

3. What is the difference between net income and gross income?

Gross income is the total amount of income before any deductions are made, while net income is the amount left after deducting expenses and taxes.

4. How do taxes affect income?

Taxes are typically deducted from gross income to determine net income. The amount of taxes paid can greatly impact the overall income of an individual or company.

5. What is the importance of calculating income?

Calculating income is important for individuals and companies to understand their financial standing and make informed decisions about budgeting, saving, and investing.

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