Mr mensah starts a job with an annual salary of $6400 which increases by $240 every year. After working for 8years,Mr. Mensah is promoted to a new with an annual salary $9500 which increases by $360 every year. Calculate:
(A)Mr Mensah salary in the 15th year of service
(B)Mr Mensah's total earnings at the end of the 15th year
A).
For the first 8 yrs
a=6400 d=240
beginning the 9th year(I.e) after the 8th year
a=9500 d=360
So 7years more to his 15th salary (I.e 15-8=7)
Thus 7th term from the 8th year
A_7=a+6d
=9500+6(360)
=11660(his 15th salary)
B.
Sum of the 1st 8 terms plus sum of the 7th term equals his total earnings
8/2(2(6400)+7(240) +7/2(2(9500)+6(360))
=131980
Nice one!
A) 6400 + 7*240 + 7*360
B) 8/2 (2*6400 + 7*240) + 7/2 (2*(6400 + 7*240) + 6*360)
Thank you very much Nsiah
To calculate Mr. Mensah's salary in the 15th year of service, we need to consider the salary progression from the start of his job until his promotion.
A) Calculating Mr. Mensah's salary in the 15th year of service:
First, let's calculate his salary from the start of his job until his promotion, which is a total of 8 years:
Starting salary = $6400
Salary increase per year = $240
Salary after 8 years = Starting salary + (Salary increase per year * number of years)
= $6400 + ($240 * 8)
= $6400 + $1920
= $8320
After 8 years, Mr. Mensah gets promoted to a new job with an annual salary of $9500, which increases by $360 every year. Now, we need to calculate his salary after the promotion.
Salary after promotion = $9500
Annual increase after promotion = $360
Now, let's calculate his salary in the 15th year:
Salary after 8 years + (Annual increase after promotion * number of years after promotion)
= $8320 + ($360 * 7)
= $8320 + $2520
= $10840
Therefore, Mr. Mensah's salary in the 15th year of service would be $10,840.
B) Calculating Mr. Mensah's total earnings at the end of the 15th year:
To calculate Mr. Mensah's total earnings at the end of the 15th year, we need to sum up his earnings from each year.
Total earnings = Earnings from the start of his job until the promotion + Earnings after the promotion (15th year salary)
Earnings from the start of the job until the promotion:
= Sum of the salaries from the start of the job to the 8th year
= (Sum of an arithmetic series with 8 terms, starting from $6400, increasing by $240 each year)
Using the formula for the sum of an arithmetic series, we can calculate this as:
Sum = (n/2) * (first term + last term)
= (8/2) * (6400 + 8320)
= 4 * 14720
= 58880
Earnings after the promotion (15th-year salary) = $10,840
Total earnings at the end of the 15th year = Earnings from the start of the job until promotion + Earnings after the promotion (15th year salary)
= 58880 + 10840
= $69720
Therefore, Mr. Mensah's total earnings at the end of the 15th year would be $69,720.