Question

Sean’s new car loan statement said he would pay $$4866.25$in interest from an interest rate of $8.5$% over $5$ years. How much did he borrow to buy his new car?

Short answer

If Sean’s new car loan statement said he would pay $$4866.25$in interest from an interest rate of $8.5$% over $5$ years then $$11450$ he borrows to buy his new car?

Step-by-step solution

Step 1. Given information    

simple interest$I=\$4866.25$

Interest rate$$\begin{gathered} r=8.5\% \\ r=0.085 \end{gathered}$$

Time$t=5$

Step 2. Principal 

Consider the principal is P

Substitute simple interest, interest rate, and time in Simple interest formula

$$\begin{gathered} I=Prt \\ 4866.25=P(0.085)\left(5\right) \\ 4866.25=0.425P \\ \frac{4866.25}{0.425}=P \\ P=11450 \end{gathered}$$

So the principal was $$11450$.

Step 3. Verification  

Simple interest of principal $$11450$with interest rate $8.5$% and time $5$years is

$$\begin{gathered} I=Prt \\ I=11450(0.085)\left(5\right) \\ I=4866.25 \end{gathered}$$

simple interest is $$4866.25$

so the principal of $$11450$is correct.