Suppose a deposit of $3,500 in a savings account that paid an annual interest rate r (compounded yearly) is worth $3,910 after 2 years.
Using the formula A=P(1+r)^t, we have 3,910=3,500(1+r) ^2Solve for r to find the annual interest rate (to the nearest tenth).
The annual interest rate, r is _____________%
so far, so good. Now you have
(1+r)^2 = 3910/3500 = 1.11714
Now just take the √ and subtract 1.
Then make that into a % rate.
To solve for r, we can rearrange the formula A = P(1+r)^t and substitute the given values:
3,910 = 3,500(1+r)^2
Divide both sides of the equation by 3,500 to isolate (1+r)^2:
(1+r)^2 = 3,910 / 3,500
Simplify the right side of the equation:
(1+r)^2 = 1.1171
Now, take the square root of both sides to solve for (1+r):
√((1+r)^2) = √1.1171
Simplify:
1 + r = 1.0566
Subtract 1 from both sides to solve for r:
r = 1.0566 - 1
r ≈ 0.0566
Thus, the annual interest rate, r, is approximately 5.7%.
To solve for the annual interest rate, r, we can use the formula A = P(1 + r)^t, where A is the final amount, P is the initial deposit, r is the interest rate (in decimal form), and t is the number of years.
In this case, we have A = $3,910, P = $3,500, and t = 2 years. We need to solve for r.
The formula becomes:
3,910 = 3,500(1 + r)^2
To solve for r, we can start by dividing both sides of the equation by 3,500:
3,910 / 3,500 = (1 + r)^2
Now, let's take the square root of both sides of the equation to eliminate the exponent:
(√(3,910 / 3,500)) = √(1 + r)^2
Simplifying the left side of the equation:
√(3,910 / 3,500) ≈ 1.112
On the right side, we can simplify the square root by removing the exponent:
√(1 + r)^2 = 1 + r
Now, we have the equation:
1.112 = 1 + r
To solve for r, subtract 1 from both sides of the equation:
1.112 - 1 = r
0.112 = r
Finally, convert r to a percentage by multiplying it by 100:
r ≈ 0.112 * 100 = 11.2%
So, the annual interest rate r is approximately 11.2%.