A professional athlete was offered a three-year contract to play with

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A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing

Hello! Yes, you ! please read below and correct my mistake!

i am using formula , and exponent meant number of years

x = \(100, 000 (1+0,20)^2\)
x = 100,000*1.44 = 144,000 +bonus 50,000 = 194,000

x = \(150,000 (1+0,1)^2\)
x = 150,000 * 1,21
x= 181,500

194,000 - 181,500 = 12,500

so why this formula doesnt work ?

Ok, GMAT quant party starts here

Hello! Yes, you ! please read below and correct my mistake!

i am using formula , and exponent meant number of years

x = \(100, 000 (1+0,20)^2\)
x = 100,000*1.44 = 144,000 +bonus 50,000 = 194,000

x = \(150,000 (1+0,1)^2\)
x = 150,000 * 1,21
x= 181,500

194,000 - 181,500 = 12,500

so why this formula doesnt work ?

Hi dave13 ,
Well, the formula didn't work because you calculated only his Year 3 salary (correctly, I might add).

You have to add the money he makes in Year 1 and Year 2.

Let's use Team K's deal.

You calculated Year 3 correctly: $144,000

You have to add
Year 1 = 100,000
Year 2 = 120,000 (= 100,000 * 1.2)
Year 3 = 144,000 (=100,00*1.44 OR 120,000*1.2)
Bonus = 50,000
--------------------
TOTAL = $414,000 for Team K's deal

Now do the same for Team L

Year 1:
Year 2: ----->(=150,000 * ____)
Year 3: $181,500 (= 150,000 * 1.21)

You've calculated a final amount FOR YEAR 3 based on accrued "interest" (really, just a percent increase) on initial salary -- but compounding interest, while cumulative, is not "additive" in the sense it needs to be here.

Hope that helps.

Let’s first determine the contract for Team K.

100,000 + 1.2(100,000) + 1.2 x 1.2(100,000) + 50,000

150,000 + 120,000 + 144,000 = 414,000

Let’s now determine the contract for team L.

150,000 + 1.1(150,000) + 1.1 x 1.1(150,000)

150,000 + 165,000 + 181,500 = 496,500

Thus, the difference is 496,500 - 414,000 = 82,500.

Answer: C