A contract specifies that Marlyn Tabungaw will receive a 5% pay increase each year for the next 30 years. She is paid PHP 120 000 the first year. What is her total lifetime salary over a 30-year period
This is just a GP with
a = 120,000
r = 1.05
So S30 = 120(1.05^30 - 1)/.05 = 79,726,617.00
To find Marlyn Tabungaw's total lifetime salary over a 30-year period, we need to calculate the salary for each year and add them up.
Marlyn's salary for the first year is PHP 120,000.
For each subsequent year, Marlyn's salary will increase by 5%. To calculate the salary for each year, we can use the following formula:
Salary = Previous Year's Salary + (Previous Year's Salary * 5%)
Let's calculate Marlyn's salary for each year:
Year 1: PHP 120,000
Year 2: PHP 120,000 + (PHP 120,000 * 5%) = PHP 120,000 + PHP 6,000 = PHP 126,000
Year 3: PHP 126,000 + (PHP 126,000 * 5%) = PHP 126,000 + PHP 6,300 = PHP 132,300
...
Year 30: Calculate using the same formula
To simplify the above calculation, we can use the concept of compound interest since each year's salary is increasing by 5%. The formula for compound interest is:
A = P(1 + r)^n
Where:
A = Final amount
P = Principal (initial amount)
r = Annual interest rate
n = Number of years
In this case, the principal (P) is PHP 120,000, the interest rate (r) is 5% expressed as a decimal (0.05), and the number of years (n) is 30.
Now, let's calculate Marlyn's total lifetime salary:
A = 120,000(1 + 0.05)^30
Calculating this equation will give us the total lifetime salary for Marlyn Tabungaw over a 30-year period.