Answer:
4.2 years
Step-by-step explanation:
assuming simple interest (see attached graphic), the following formula applies.
A = P [ 1 + (rt) ] where,
A = final amount = $3,000
P = Principal Amount = $2,000
r = annual rate = 12% = 0.12
t = time in years
Substituting the above values into the formula gives,
3000 = 2000 [ 1 + (0.12)(t) ] (divide both sides by 2000)
3000/2000 = 1 + 0.12t
(3/2) = 1 + 0.12t (subtract 1 from both sides and rearrange)
0.12t = (3/2) - 1
0.12t = (1/2) (note 1/2 = 0.5)
0.12t = 0.5 (divide both sides by 0.12)
t = 0.5 / 0.12
t = 4.166666666667
t = 4.2 years (1 dec. pl)
Answer:
It is going to take 4.2 years for $2,000 to reach $3,000.
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 problem, we have that:
[tex]P = 2000, I = 0.12[/tex]
We want to find t when [tex]T = 3000[/tex]
So
[tex]T = E + P[/tex].
[tex]3000 = E + 2000[/tex]
[tex]E = 1000[/tex]
-----------
[tex]E = P*I*t[/tex]
[tex]1000 = 2000*0.12t[/tex]
[tex]0.12t = 0.5[/tex]
[tex]t = \frac{0.5}{0.12}[/tex]
[tex]t = 4.2[/tex]
It is going to take 4.2 years for $2,000 to reach $3,000.
