Question

Aaron was offered a job that paid a salary of \$57,000$57,000 in its first year. The salary was set to increase by 1% per year every year. If Aaron worked at the job for 29 years, what was the total amount of money earned over the 29 years, to the nearest whole number?

Answer 1

Answer:

The total amount received is: $1906650

Step-by-step explanation:

Given

$a = \ 57000$ --- initial

$b = 1\%$ --- rate

$n = 29$ --- time

Required

Determine the total amount at the end of 29 years

The given question is an illustration of geometric progression, and we are to solve for the sum of the first n terms

Where $n = 29$

$r = 1 + b$

$r = 1 + 1\%$

Express percentage as decimal

$r = 1 + 0.01$

$r = 1.01$

The required is the calculated using:

$S_n = \frac{a(r^n - 1)}{r - 1}$

So, we have:

$S_n = \frac{57000 * (1.01^{29} - 1)}{1.01 - 1}$

$S_n = \frac{57000 * (1.3345- 1)}{0.01}$

$S_n = \frac{57000 * 0.3345}{0.01}$

$S_n = \frac{19066.5}{0.01}$

$S_n = 1906650$

The total amount received is: $1906650