Question

If your starting salary were $50,000 and you received a 4% 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?

Answer 1

Answer-

The total amount you would have earned over the first 16 years is $90047.20

Solution-

The exponential function that would given the growth is,

$P'=P(1+r)^t$

Where,

P' = Future value,

P = Current value = $50000

r = rate of change = 4% = 0.04

t = time = 15 year (not 16 because the the increment occurs at year end and we want to get the value at the beginning of 16th year)

Putting the values,

$P'=50000(1+0.04)^{15}$

$=50000(1.04)^{15}$

$=90047.20$

Therefore, the total amount you would have earned over the first 16 years is $90047.20

Answer 2

n = 16 

50000(1 + 1.04 + 1.04^2 + 1.04^3 + .... + 1.04^15) = 50000 * (1.04^16 - 1) / (1.04 - 1) = 1,091,226.56 

Final year's salary = 90047.17 

86,583.82 * 1.04 = 90047.17 

There are only 15 table when there should be 16.

a_N = 50000(1.04)^15 = 90047.17 

And if we add 90047.17 to the previous total of 1001179.38 we get 

$1,091,226.55