Solve the problem.
-If a $6000 investment compounded to $7128.60 after 2 years, compounded annually, find the annual interest rate of the investment. Use the formula, A
A) 900%
B) 9%
C) 0.9%
D) 90%

Question

Solve the problem.
-If a $6000 investment compounded to $7128.60 after 2 years, compounded annually, find the annual interest rate of the investment. Use the formula, A 
A) 900% 
B) 9% 
C) 0.9% 
D) 90%

Quizplus · Accepted Answer

Using the given formula, $A=P\left(1+\frac{r}{n}ight)^{nt}$ where:
A = Amount at the end of the investment period ($7128.60)
P = Principal or initial investment ($6000)
r = Annual interest rate (unknown)
n = Number of times compounded per year (1 for annually)
t = Time in years (2)

Substituting the given values, we get:
$7128.60=6000\left(1+\frac{r}{1}ight)^{1	imes2}$

Solving for r, we get:
$r= \frac{(7128.60/6000)^{1/2}-1}{1}	imes 100\% \approx 0.09 	imes 100\% \approx 9\%$

Therefore, the annual interest rate of the investment is 9%. Using the formula A = P(1 + r/n)^(nt), where A is the resulting amount, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years:

$7128.60 = $6000(1 + r/1)^(1*2)
$7128.60/$6000 = (1 + r)^2
1.1881 = (1 + r)^2
Taking the square root of both sides, we get:
1.0909 = 1 + r
r = 0.0909 or 9%

Therefore, the annual interest rate of the investment is 9%.

Solve the Problem. -If a $6000 Investment Compounded to $7128.60 After 2 Years