Problem

The principal $P$ is borrowed and the loan's future value $A$ at time $t$ is given. Determine the loan's simple interest rate $r$.
\[
P=\$ 2000.00, A=\$ 2720.00, t=4 \text { years }
\]
\% (Round to the nearest tenth of a percent as needed.)

Answer

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Answer

Final Answer: The loan's simple interest rate is \(\boxed{9.0\%}\).

Steps

Step 1 :We are given the principal amount (P) as $2000.00, the future value of the loan (A) as $2720.00, and the time (t) as 4 years. We are asked to find the simple interest rate (r).

Step 2 :The formula for simple interest is given by \(A = P(1 + rt)\), where A is the future value of the loan, P is the principal amount, r is the annual interest rate in decimal, and t is the time the money is invested for in years.

Step 3 :We can rearrange this formula to solve for r: \(r = \frac{A - P}{Pt}\).

Step 4 :Substituting the given values into this formula, we get \(r = \frac{2720 - 2000}{2000 \times 4}\).

Step 5 :Solving this equation, we find that \(r = 0.09\).

Step 6 :To convert this decimal to a percentage, we multiply by 100, giving us an interest rate of 9.0%.

Step 7 :Final Answer: The loan's simple interest rate is \(\boxed{9.0\%}\).

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