abi takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. to…

abi takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. to the nearest dollar, how much does abi make over the first six years?\n$600,000\n$618,000\n$646,841\n$716,431

abi takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. to the nearest dollar, how much does abi make over the first six years?\n$600,000\n$618,000\n$646,841\n$716,431

Answer

Explanation:

Step1: Identify the series type

This is a geometric - series problem. The first term $a = 100000$ and the common ratio $r=1 + 0.03=1.03$. The number of terms $n = 6$.

Step2: Use the sum formula for a geometric series

The sum formula for a geometric series is $S_n=\frac{a(r^n - 1)}{r - 1}$. Substitute $a = 100000$, $r = 1.03$, and $n = 6$ into the formula: $S_6=\frac{100000\times(1.03^6 - 1)}{1.03 - 1}$.

Step3: Calculate $1.03^6$

$1.03^6=1.03\times1.03\times1.03\times1.03\times1.03\times1.03\approx1.194052$.

Step4: Calculate the numerator

$100000\times(1.03^6 - 1)=100000\times(1.194052 - 1)=100000\times0.194052 = 19405.2$.

Step5: Calculate the denominator

$1.03 - 1=0.03$.

Step6: Calculate the sum

$S_6=\frac{19405.2}{0.03}=646840\approx646841$.

Answer:

$646,841$