Respuesta :
Answer:
She would need to leave the money in her account for 6 years and 8 months.
Step-by-step explanation:
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 question:
She put 500 into the saving account, so [tex]P = 500[/tex]
7.5% annual interest, so [tex]I = 0.075[/tex]
Saving $750. So we need T = 750.
Interest earned:
[tex]T = E + P[/tex]
[tex]750 = E + 500[/tex]
[tex]E = 250[/tex]
How long to earn $250 in interest, in years:
[tex]E = P*I*t[/tex]
[tex]250 = 500*0.075*t[/tex]
[tex]t = \frac{250}{500*0.075}[/tex]
[tex]t = 6.67[/tex]
Converting to months:
6.67 years, that is, 6 years and (2/3) of an year.
An year has 12 months.
(2/3)*12 = 8.
So
She would need to leave the money in her account for 6 years and 8 months.
