Question

Two years ago, Ben borrowed $150 from his brother to buy a CD player. He agreed to pay $15 in interest. What is the simple annual interest rate for this loan?

Answer 1

`\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$15\\ P=\textit{original amount deposited}\to& \$150\\ r=rate\to r\%\to (r)/(100)\\ t=years\to &2 \end{cases} \\\\\\ 15=150\cdot r\cdot 2\implies \cfrac{15}{150\cdot 2}=r\implies \cfrac{1}{10}=r \\\\\\ r\cdot 100\implies \stackrel{\%}{10}`

Answer 2

The simple annual interest rate is 5 %.

Explanation:

Simple interest formula is,

`I=(P* r* t)/(100)`

Where, P is the principal amount,

r is the rate per period,

t is the number of periods,

Here, P = $ 150,

I = $ 15,

t = 2 years,

By substituting the values,

`15=(150* r* 2)/(100)`

`15=(300r)/(100)`

`15=3r`

`\implies r = 5\%`

Hence, the simple annual interest rate is 5 %.