Question

K

A chef at a Peruvian restaurant received increasing annual salaries over 3 years: $48,000, $50,400,
and $52,920. For the next 3 years, the chef's annual salary will increase by the same percentage.
What is the chef's total amount of salary earnings over the 6 years? Use the formula below, where
a is the first term in the sequence of annual salaries. Round your answer to the nearest dollar.
Sn =
a(1-r")
1-r

Answer 1

The chef's total amount of salary earnings over the 6 years can be calculated using the formula Sn = a(1-rn)/(1-r). Substitute the values and calculate, the chef's total amount of salary earnings over the 6 years is approximately $-13,248.

Step-by-step explanation:

The chef's total amount of salary earnings over the 6 years can be calculated using the formula:

Sn = a(1-rn)/(1-r)

where:

• Sn is the total amount of salary earnings
• a is the first term in the sequence of annual salaries
• r is the common ratio
• n is the number of years

In this case, the first term is $48,000 and the common ratio can be found by dividing the second term by the first term: $50,400 / $48,000 = 1.05.

Therefore, the common ratio is 1.05.

Using the formula, we can substitute the values and calculate:

S6 = $48,000(1-1.056)/(1-1.05)

S6 = $48,000(1-1.3401)/(0.05)

S6 = $48,000(-0.3401)/(0.05)

S6 ≈ $-13,248

Therefore, the chef's total amount of salary earnings over the 6 years is approximately $-13,248.