Mr. Mensah starts a job with an annual salary of $240,every year. After working for eight years, Mr Mensah is promoted to a new post with an annual salary of $9500 which increases by $360 every year,calculate (a) Mr Mensah's salary in the fifteenth year of service. (B) Mr Mensah's total earnings at the end of the fifteenth year of service.
Confusing question.
Mr. Mensah starts a job with an annual salary of $240,every year ?????
Do we just ignore the first 8 years?
Does he get $9500 in year 8 ?
To calculate Mr. Mensah's salary in the fifteenth year of service, we need to determine how much his salary increases each year for both his initial job and the new post.
For the initial job:
- Mr. Mensah's salary starts at $240.
- It remains the same for 8 years.
For the new post:
- Mr. Mensah's salary starts at $9500.
- It increases by $360 every year.
To calculate Mr. Mensah's salary in the fifteenth year of service (a), we need to determine the amount by which his salary increases each year for the new post. Since his salary remains the same for the initial 8 years, we will focus on the salary increase for the new post.
The salary increase for the new post is $360 per year. Therefore, in the fifteenth year, his salary will have increased by $360 multiplied by the number of years (15 - 8) = $360 x 7 = $2520.
Hence, Mr. Mensah's salary in the fifteenth year of service (a) is $9500 + $2520 = $12020.
To calculate Mr. Mensah's total earnings at the end of the fifteenth year of service (b), we need to consider his earnings from both his initial job and the new post.
For the initial job:
- His salary is $240 per year.
- He works for 8 years.
- Therefore, his total earnings from the initial job are $240 x 8 = $1920.
For the new post:
- His salary starts at $9500.
- It increases by $360 per year.
- He works for 7 years (15 - 8).
- To calculate the total earnings, we need to calculate the sum of an arithmetic progression with the first term ($9500), common difference ($360), and number of terms (7).
Using the formula for the sum of an arithmetic progression:
Sum = (n/2) * (2a + (n-1)d)
Where:
n = number of terms
a = first term
d = common difference
In this case:
n = 7
a = $9500
d = $360
Sum = (7/2) * (2($9500) + (7-1)($360))
Sum = 3.5 * (19000 + 6 * 360)
Sum = 3.5 * (19000 + 2160)
Sum = 3.5 * 21160
Sum = $74060
Hence, Mr. Mensah's total earnings at the end of the fifteenth year of service (b) are $1920 + $74060 = $75980.