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
