Answer:
$15,000
Step-by-step explanation:
To determine how much Jackson needs to invest to earn $50 a month in interest from his simple interest savings account, we need to use the simple interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Simple Interest Formula}}\\\\I = Prt\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$I$ is the total interest.}\\ \phantom{ww}\bullet\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\textsf{$r$ is the annual interest rate (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\\ \end{array}}[/tex]
Since Jackson wants to earn $50 per month in interest, his annual interest goal is:
[tex]\textsf{Annual interest}=\$50\textsf{ per month} \times 12\textsf{ months per year} \\\\ \textsf{Annual interest}=\$600[/tex]
Therefore, the values of I, r and t for one year are:
- I = $600
- r = 4% = 0.04
- t = 1 year
Substitute the values into the simple interest formula and solve for P:
[tex]600=P \times 0.04 \times 1 \\\\\\600=0.04P\\\\\\\dfrac{0.04P}{0.04}=\dfrac{600}{0.04}\\\\\\P=15000[/tex]
So, Jackson will need to invest $15,000 in his savings account to earn $50 a month in interest.
