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?

Related Precalculus Mathematics Homework Help News on Phys.org
HallsofIvy
Homework Helper
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: $(1.05)^{24}(5000)$.

$$a_1=5000$$

$$a_2=a_1+a_1*\frac{5}{100}=a_1*1.05$$

$$a_3=a_1*1.05 + a_1*1.05*0.05=a_1*1.05(1 + 0.05)=a_1*1.05*1.05$$

$$a_4=a_1*1.05*1.05*1.05$$

$$...................................$$

$$a_{n+1}=a_1*(1.05)^{n}$$

So a25=5000*(1.05)24

Regards.

Last edited:
Is 1.05 constant?

Is 1.05 constant?
Yep, its a constant.

HallsofIvy
Homework Helper
It's certainly not going to change!

ok. where is that 1.05 come from?

ok. where is that 1.05 come from?
If you see my way of solving the problem, you'll spot that

$$a_2=a_1+a_1*\frac{5}{100}=a_1(1+\frac{5}{100})=a_1\frac{100+5}{100}=a_1\frac{105}{100}=a_1*1.05$$

See now where it comes from?

HallsofIvy