Question

suppose that you borrow $1000.00 from a friend and promise to pay back $1820.00 in 4 years. what simple interest rate will you pay?

the simple interest rate is \\(\square\\)% (round to the nearest tenth as needed )

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is $A = P(1 + rt)$, where $A$ is the amount owed, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. We know $A = 1820$, $P = 1000$, and $t = 4$. We need to solve for $r$.

Step2: Substitute values into the formula

Substitute the known values into the formula: $1820 = 1000(1 + r\times4)$.

Step3: Solve for the term in parentheses

First, divide both sides by 1000: $\frac{1820}{1000}=1 + 4r$. Simplify the left side: $1.82 = 1 + 4r$.

Step4: Isolate the term with $r$

Subtract 1 from both sides: $1.82 - 1 = 4r$. So, $0.82 = 4r$.

Step5: Solve for $r$

Divide both sides by 4: $r=\frac{0.82}{4}=0.205$.

Step6: Convert to percentage

To convert the decimal to a percentage, multiply by 100: $r = 0.205\times100 = 20.5\%$.

Answer:

20.5