# Emma takes a job with a starting salary of $42,000. Her salary increases by 4% at the beginning of each year. What will be Emma's salary, to the nearest thousand dollars, at the beginning of year 10? ##### 2 Answers Mar 25, 2016 Alternative solution: #### Explanation: We can use geometric sequences to calculate this. In a geometric series, the formula for ${t}_{n}$is ${t}_{n} = a \times {r}^{n - 1}$. "r" is the rate of change, n is the number of terms and a is the first term. Reading the question, we find the following. $r = 1.04$(since 100% + 4%) a =$42 000

$n = 10$

Therefore, we are solving for ${t}_{n}$

${t}_{10} = 42000 \times {1.04}^{9}$

${t}_{10} = 59779.10$

Emma's salary would be $59779.10 after 10 years. Practice exercises: John gets a job where the base salary is of $54 322. His salary increases by 5.7% each year, until a maximum of 10 years. Find his salary after 16 years.

Mar 25, 2016

Here is the third solution.
$60 , 000$ Rounded to nearest thousand dollar

#### Explanation:

Let Emma's salary at the beginning of $10 t h$ year be =$x. Rate of increase per year 4%=(1+4/100) General expression for salary at the beginning of $n t h$year is given as $x =$$\text{Initial Salary"xx(1+"% increase per year"/100)^"no of completed years}$Number of completed years at the beginning of $10 t h$year $= 9$Inserting given values we obtain $x = 42000 \times {\left(1 + \frac{4}{100}\right)}^{9}$or $x = 42000 \times {\left(1.04\right)}^{9}$or $x = 59779.10$rounded to nearest penny. $x = 60000\$ Rounded to nearest thousand dollar