Question

Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
42{,}000\left(\dfrac{1-0.04^n}{0.96}\right)42,000(
0.96
1−0.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 0, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice B)
B
42{,}000\left(\dfrac{1-1.04^n}{-0.04}\right)42,000(
−0.04
1−1.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, minus, 0, point, 04, end fraction, right parenthesis

(Choice C)
C
42{,}000\left(\dfrac{1-1.04^n}{0.96}\right)42,000(
0.96
1−1.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice D)
D
42{,}000\left(\dfrac{1-0.96^n}{-0.04}\right)42,000(
−0.04
1−0.96
n

​
)

Answer 1

Answer:

$A=42000(1.04)^n$

Step-by-step explanation:

This is a compound interest formula expressed as:

$A=P(1+i)^n$

Where:

• $n$ is time in years
• $i$ is the rate of interest
• $A$ is the accumulated amount after n years
• $P$ is the initial amount.

#We substitute the given values to determine amount after n years as follows:

$A=P(1+i)^n\\\\=42000(1+0.04)^n\\\\=42000(1.04)^n$

Hence, the amount earned after n years is given by the expression $A=42000(1.04)^n$