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

T = 40000 + 40000(1.03) + 40000(1.03)^2 + ... + 40000(1.03)^15

Multiply the above equation by 1.03 giving

1.03(T) = 40000(1.03) + 40000(1.03)^2 + 40000(1.03)^3 + ... + 40000(1.03)^15 + 40000(1.03)^16

Now subtract the first equation from the second to give

0.03T = 40000(1.03)^16 - 40000

0.03T = 40000(1.03^16 - 1)

0.03T = 24188.26

T = 24188.26 / 0.03 = $806275.25

Answer 2

Answer: Hello there!

If you have an initial amount of A, and you increase it by 3%, the math that you need to do is:

B = A + 0.03*A = 1.03*A

now let's apply it to the work:

the first year you have $40,000

the second year you have 1.003*$40,000  

the third year you have 1.003*1.003*$40,000

and so on, this augment can be modeled as:

P(t) = $40,000*1.003^(t - 1)

where t is the number of years, t= 1 is the first year in the work, t = 2 is the second year in work, and so on.

the total amount earned in the first 16 years of work is:

P(1) + P(2) + ...... + P(15) + P(16)  

this is equal to

=$40,000 + $40,000*1.003 + ....

= $40,000*( 1 + 1.003 + 1.003^2 + 1.003^3 + ..... + 1.003^14 + 1.003^15)  

you can solve the parenthesis using a calculator, and get:

= $40,000*16.365= $654603.579

now we want to round it to the nearest dollar, the first number after the decimal point is a 5, so we need to round up:

the total amount that you earned in the first 16 years is:

P = $654604