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

Answer:

The simple annual interest rate is 5 %.

Step-by-step explanation:

Simple interest formula is,

$I=\frac{P\times r\times t}{100}$

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,

$15=\frac{150\times r\times 2}{100}$

$15=\frac{300r}{100}$

$15=3r$

$\implies r = 5\%$

Hence, the simple annual interest rate is 5 %.

Answer 2

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