when P dollars is invested at interest rate (I), compounded annually, for (t) years, the investment grows to (A) dollars, where A=P(1+I)^3. Find the interest rate if $40,960 grows to $49,130 in 3 yrs.
A=P(1+I)^3
You mean A=P(1+I)^t
t just happens to be 3 years here
49130 = 40960 (1+i)^3
1.19946 = (1+i)^3
take cube root
1 + i = 1.0625
or i = 6.25 %
To find the interest rate (I), we can use the formula A = P(1+I)^t, where A is the final amount, P is the initial principal, I is the interest rate, and t is the number of years.
Given that A = $49,130, P = $40,960, and t = 3, we can substitute these values into the formula and solve for I.
$49,130 = $40,960(1+I)^3
Dividing both sides of the equation by $40,960, we get:
1.2 = (1+I)^3
To solve for (1+I)^3, we can take the cube root of both sides of the equation:
∛(1.2) = 1+I
Subtracting 1 from both sides:
∛(1.2) - 1 = I
Using a calculator, we can find that ∛(1.2) is approximately equal to 1.0905.
Therefore, the interest rate (I) is approximately equal to:
I = 1.0905 - 1 = 0.0905
So, the interest rate is approximately 9.05%.