The salary scale of a company CEO start at #1million per annum. A rise of 2000 is given at the end of each year. Find the total amount of money earned in 15 years.
The total amount of money earned in 15 years is #31 million.
To find the total amount of money earned in 15 years, we need to calculate the salary for each year and then sum them up.
Given that the CEO's salary starts at #1 million per annum and there is a rise of #2000 at the end of each year, we can calculate the salary for each year as follows:
Year 1: #1,000,000
Year 2: #1,000,000 + #2,000 = #1,002,000
Year 3: #1,002,000 + #2,000 = #1,004,000
...
Year 15: #1,000,000 + (#2,000 x 14) = #1,000,000 + #28,000 = #1,028,000
To calculate the total amount of money earned in 15 years, we need to sum up the salaries for each year. We can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term)
where n is the number of terms (in this case, 15), the first term is #1,000,000, and the last term is #1,028,000.
Using the formula, we can calculate the total amount of money earned as follows:
Sum = (15/2) * (1,000,000 + 1,028,000)
= 7.5 * 2,028,000
= 15,210,000
Therefore, the CEO will earn a total of #15,210,000 in 15 years.
To find the total amount of money earned in 15 years, we can use the arithmetic progression formula.
First, let's calculate the annual salary for each year.
The initial salary is $1 million per annum, and a rise of $2000 is given at the end of each year.
The formula for the nth term of an arithmetic progression is:
aₙ = a₁ + (n - 1)d
Where:
aₙ is the nth term
a₁ is the first term
n is the number of terms
d is the common difference
In this case:
a₁ = $1,000,000
d = $2,000
n = 15 (as we want to calculate for 15 years)
Using the formula, we can calculate the salary for each year:
aₙ = $1,000,000 + (n - 1) * $2,000
Let's calculate the salary for each year and sum them up to find the total amount of money earned in 15 years.
Year 1: $1,000,000
Year 2: $1,000,000 + $2,000 = $1,002,000
Year 3: $1,002,000 + $2,000 = $1,004,000
...
Year 15: $1,000,000 + (15 - 1) * $2,000 = $1,000,000 + $28,000 = $1,028,000
To calculate the sum, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (2a₁ + (n - 1)d)
In this case:
n = 15
a₁ = $1,000,000
d = $2,000
Sum = (15/2) * (2 * $1,000,000 + (15 - 1) * $2,000)
Simplifying the equation:
Sum = (15/2) * (2,000,000 + 14 * 2,000)
Sum = (15/2) * (2,000,000 + 28,000)
Sum = (15/2) * (2,028,000)
Sum = 7,620,000
Therefore, the total amount of money earned in 15 years is $7,620,000.