a man gets an employment of rs 6500 per month with an annual increment of rs 500.what will be his monthly salary after 15 years and what will be the total amount he earns in 15 years
Answers
second year he gets 78500
third year he gets 79000
and so on
His annual incomes are in arithmatic progression.
a = 78000
d = 500
n = 15
a₁₅ = a+(n-1)d
= 78000 + 14(500)
= 78000 + 7000
= 85000
he gets 85000 as annual income after 15 years
he gets 13500 as monthly salary after 15 years
total amount he earns in 15 years = n/2 [ 2a + (n-1)d ]
total amount = 15/2 [156000 + 7000 ]
total amount = 12,22,500 rs
Answer:
his monthly income during the 15th year is 13,500.
his total yearly income, after adding up all 15 years of yearly income, is 1,800,000.
Step-by-step explanation:
he starts off at 6500 each month and gets an annual increase of 500 a month for each year that he's with the firm.
this occurs for 15 years.
his monthly salary in the 15th year of service will be 6500 + 14 * 500 = 162,000.
by the end of the first year, he will have earned 12 * 6500 = 78,000
by the end of the second year, he will have earned 12 * 7000 = 84,000
by the end of the third year, he will have earned 12 * 7500 = 90,000
etc...
this problem uses the formulas for an arithmetic sequence.
those formulas are:
An = A1 + (n-1) * d
Sn = n * (A1 + An) / 2
you would use the An formula to find out what his monthly income is in the 15th year.
you would get:
A15 = 6500 + 14 * 500 = 13,500. that's his monthly salary in the 15th year.
for all of the first year, he made 6500 * 12 = 78,000
for all of the fifteenth year, he made 13,500 * 12 = 162,000
the sum of his total income for all 15 years uses the Sn formula of Sn = n * (A1 + An) / 2
this formula becomes S15 = (78,000 + 162,000) / 2
the result is the S15 = 1,800,000
....that's his total income for all 15 years.