Find the final hourly wage if a $ 10.50 starting wage is increased by 4% each year for 9 years. Half the raise is given every 6 months

Question

Used in pre-algebra and not sure of the steps to solve this problem

Answer 1

Note: The phrasing of the problem is confusing. Is the raise on starting wage or on the current wage? The solution below assumes that raise is on the current wage and not on the starting wage.

 

This problem is similar to compound interest problem.

 

FV = Future Value

PV = Present Value

r = Interest Rate annually

n = Number of compounding periods in a year

t = Number of Years

 

FV = PV (1 + r / n)^t = 10.50(1 + 0.04/2)⁹ = 10.50(1.02)⁹ = 10.50(1.195) = 12.55

 

Or you can use simple but laborious procedure below if compounding hasn't been covered yet in your pre-algebra course.

 

The raise is given every six months so there are two raises each year. As total raise in a year is 4% (0.04 in decimal), the raise for each six month period will be half of 4% = 2% (0.02  in decimal).

 

At the start, Wage = $10.50

Wage at 6 month = start wage + raise = $10.50 + ($10.50 * 0.02) = $10.50 + 0.21 = $10.71

Wage at 1 year = Wage at 6 month + raise = $10.71 + ($10.71 * 0.02) = $10.71 + 0.2142 = $10.91

Wage at 1 year 6 months = Wage at 1 year + raise = $10.91 + ($10.91 * 0.02) = $11.13

Do the same calculations for every six months until you get the wage at the end of 9 years.