Question

jen is going to save $3,000 for retirement over 20 years. which option should jen go with? her two options are: option a is a simple interest account with a 1.85% annual interest rate option b is a compound interest account with a 1.75% annual interest rate

Explanation:

Step1: Calculate Simple Interest for Option A

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.
Given $P = 3000$, $r = 0.0185$, $t = 20$.
$I = 3000 \times 0.0185 \times 20$
$I = 3000 \times 0.37$
$I = 1110$
Total amount for Option A: $3000 + 1110 = 4110$

Step2: Calculate Compound Interest for Option B

The formula for compound interest is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time the money is invested for in years.
Given $P = 3000$, $r = 0.0175$, $t = 20$.
$A = 3000(1 + 0.0175)^{20}$
First, calculate $(1 + 0.0175)^{20} \approx 1.414778$ (using a calculator for the exponentiation)
Then, $A = 3000 \times 1.414778 \approx 4244.33$

Step3: Compare the two amounts

Option A total: $4110$
Option B total: $\approx 4244.33$
Since $4244.33 > 4110$, Option B gives a higher total amount.

Answer:

Jen should go with Option B (a compound interest account with a 1.75% annual interest rate) as it results in a higher total amount ($\approx 4244.33$) compared to Option A ($4110$) after 20 years.