Question

If your starting salary were $40,000 and you received a 3% increase at the end of every year for 15 years, what would be the total amount, in dollars, you would have earned over the first 16 years that you worked?
Round your answer to the nearest whole dollar.

Answer 1

658000

Answer 2

Work it out. What's your plan?

40000 + 40000*(1.03) + 40000*(1.03)^2 + ... + 40000*(1.03)^15

Add it all up.

Answer 3

where did you get 1.03?

Answer 4

ok,so you do 40000x16,add 1200 on for every year for the next 15 years

Answer 5

don't you use sn=a1(1-r^n)/1-r ?

Answer 6

"received a 3% increase "

40000*0.03 is the increase percentage each year.
40000*1.03 is the total after the increase each year.

Answer 7

No if your looking for strategy then sorry,i just do these in my head and forget how to explain it elseware.

Answer 8

The formula will do you no good if you didn't see the value of 'r' in the problem statement. It will also do you no good if you're not sure it's the right one.

Personally, and not everyone agrees with me on this, I refuse to learn those formulas. It is just as easy and just as fast to learn how to build them on the fly. Doing so absolutely eliminates these questions about which one and how to use it. Again, that is my opinion.

Answer 9

We've established that r = 1.03. What is n?

Answer 10

16?

Answer 11

Let's see what you get.

Answer 12

24187

Answer 13

What is that? It's at least $40,000 * 16 = $640,000

Please show your intermediate results. What is r^16?

Answer 14

So i was right,why bother with the formula,(don't get me wrong,it great to learn) but i solved this problem with just common sense.

Answer 15

?? $658,000 is very short. Better get more common sense. :-)

Answer 16

?,Ok,take a look,40000x16+18000=658,000

Answer 17

18,000 is three percent over the next 15 years.

Answer 18

s16=40,000(1-1.03^16) / 1-1.03=40,000(1-1.60) / -0.03=40000(-0.6) / -0.03 = -24000 / -0.03 = 800000

I failed.

Answer 19

Hold that thought

Answer 20

Use more decimal places. That's all.

1.03^16 = 1.6047064390987875179380544409792

\(log_{10}(40000)=4.6ish\) so use at least 6 decimal places.

Answer 21

24187?

Answer 22

K,you'll have to explain how you keep getting such a low number.

Answer 23

You just said 800000. Then you reported the answer as 24187. That makes no sense at all.

Do what you already did. Just use more decimal places.

s16=40,000(1-1.03^16) / (1-1.03)

Actually, with accumulation, it's a little easier to turn them around. Same answer, just less arithmetic to go wrong.

s16=40,000(1.03^16 - 1) / (1.03 - 1)

Answer 24

s16=40000(1-1.03^16) / 1- 1.03
= 40000(1-1.604706439) / -0.03
= 40000(-0.604706439) / -0.03
= -24188.25756 / -0.03
=806275

I got something different this time...

Answer 25

That's it. You will almost always get something different when you switch from making mistakes to NOT making mistakes.

Answer 26

haha thanks :)

Answer 27

@deadmanwalking

40000x16+18000=658,000

This is strange. What is the 18000?

Answer 28

me forgetting that i suck at percents,sorry,i also made a mistake and forgot to add a few numerals into certain parts of the equation.

Answer 29

please ignore my posts completely if you haven't already.