Question

1. harut owed $12,749 after he graduated college. they were giving him a 4.5% apr. at the end of a year, assuming harut doesn’t pay any of it back yet, how much will harut owe?

Explanation:

Step1: Identify the formula for simple interest

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. The total amount owed $A$ is the principal plus the interest, so $A = P + I = P(1 + rt)$.

Step2: Convert the APR to a decimal

The APR is 4.5%, so $r = \frac{4.5}{100} = 0.045$. The principal $P = 12749$ and the time $t = 1$ year (since it's at the end of a year).

Step3: Calculate the total amount owed

Substitute the values into the formula $A = P(1 + rt)$. So $A = 12749\times(1 + 0.045\times1)$. First, calculate the value inside the parentheses: $1 + 0.045 = 1.045$. Then multiply by the principal: $12749\times1.045$.

Calculate $12749\times1.045$:
\[

$$\begin{align*} 12749\times1.045&=12749\times(1 + 0.04 + 0.005)\\ &=12749\times1 + 12749\times0.04 + 12749\times0.005\\ &=12749 + 509.96 + 63.745\\ &=12749 + 573.705\\ &=13322.705 \end{align*}$$

\]

Answer:

$\$13322.71$ (rounded to the nearest cent)