Answer:
He will have to invest $20,519.84 today.
Step-by-step explanation:
We can solve this question using the simple interest formula:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
In this problem, we have that:
[tex]I = 0.077, t = 6, T = 30,000[/tex]
So
[tex]T = E + P[/tex].
[tex]E + P = 30000[/tex]
[tex]E = 30000 - P[/tex]
So
[tex]E = P*I*t[/tex]
[tex]30000 - P= P*0.077*6[/tex]
[tex]30000 - P = 0.462P[/tex]
[tex]1.462P = 30000[/tex]
[tex]P = \frac{30000}{1.462}[/tex]
[tex]P = 20519.84[/tex]
He will have to invest $20,519.84 today.
