mr mensah starts a job with an annual salary of $6400 which increases by $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 mr mensah salary in the fifteenth year of service and mr mensah total earnings at the end of the fifteenth year of service
The way I read it, you have 8 terms of the first AP, with a = 6400 and d=240
plus 7 terms of a second AP with a = 9500 and d=360
The 15th year would be the 7th term of series #2
term7 = 9500+6(360) = ....
Use your sum of terms formula to find the two sums and add them.
Please solve it with full details
Yes
To calculate Mr. Mensah's salary in the fifteenth year of service, we need to find the annual salary after working for 15 years.
First, let's calculate the number of years Mr. Mensah worked at his initial salary:
Number of years at initial salary = 15 - 8 = 7 years
Next, let's calculate the salary increase for each year at the initial post:
Salary increase per year at the initial post = $240
Mr. Mensah's salary at the end of the eighth year = Initial salary + (Number of years at initial salary * Salary increase per year)
Mr. Mensah's salary at the end of the eighth year = $6400 + (7 * $240) = $6400 + $1680 = $8080
Now, let's calculate the number of years Mr. Mensah worked at his new post:
Number of years at new post = 15 - 8 = 7 years
Next, let's calculate the salary increase for each year at the new post:
Salary increase per year at the new post = $360
Mr. Mensah's salary at the end of the fifteenth year = New post salary + (Number of years at new post * Salary increase per year)
Mr. Mensah's salary at the end of the fifteenth year = $9500 + (7 * $360) = $9500 + $2520 = $12020
Therefore, Mr. Mensah's salary in the fifteenth year of service is $12,020.
To calculate Mr. Mensah's total earnings at the end of the fifteenth year of service, we need to sum up his earnings at the initial post and the new post.
Mr. Mensah's total earnings at the end of the fifteenth year of service = Total earnings at the initial post + Total earnings at the new post
Total earnings at the initial post:
Total earnings at the initial post = (Initial salary + Mr. Mensah's salary at the end of the eighth year) * Number of years at initial salary
Total earnings at the initial post = ($6400 + $8080) * 7 = $14,280 * 7 = $99,960
Total earnings at the new post:
Total earnings at the new post = (New post salary + Mr. Mensah's salary at the end of the fifteenth year) * Number of years at new post
Total earnings at the new post = ($9500 + $12,020) * 7 = $21,520 * 7 = $150,640
Mr. Mensah's total earnings at the end of the fifteenth year of service = Total earnings at the initial post + Total earnings at the new post
Mr. Mensah's total earnings at the end of the fifteenth year of service = $99,960 + $150,640 = $250,600
Therefore, Mr. Mensah's total earnings at the end of the fifteenth year of service is $250,600.