Respuesta :
Answer:
You need to invest at the rate of 11.46% a year to hit your goal.
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]T = 1750, P = 1200, t = 4[/tex]
We want to find I. So
First we have to find E
[tex]T = E + P[/tex].
[tex]1750 = E + 1200[/tex].
[tex]E = 550[/tex]
Now, we apply at the formula.
[tex]E = P*I*t[/tex]
[tex]550 = 1200*I*4[/tex]
[tex]4800I = 550[/tex]
[tex]I = \frac{550}{4800}[/tex]
[tex]I = 0.1146[/tex]
You need to invest at the rate of 11.46% a year to hit your goal.
The rate is 9.09%.
Compound interest
Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Given
You currently have $1,200 and you need $1,750 in 4 years.
To find
The rate does you need to invest at to hit your goal.
How to achieve the rate do you need to invest at to hit your goal?
We know the formula
[tex]\rm Amount = Principal (1 + \dfrac{r}{100})^{time}[/tex]
Here we have
Amount = $1,700
Principal = $1200
Rate = r%
Time = 4yr
Then
[tex]\begin{aligned} 1700 &= 1200 (1 +\dfrac{r}{100} )^{4}\\1.4167 &= \dfrac{100+r}{100})^{4}\\1.091 &= \dfrac{100+r}{100}\\109.1 &= 100 + r\\r &= 9.09\\\end{aligned}[/tex]
Thus the rate is 9.09%.
More about the compound interest link is given below.
https://brainly.com/question/25857212
