Question

Jack borrowed $\$1000$ from a friend for a simple interest rate of $6\%$ per annum. He returned his friend $\$1300.$ How long did Jack take to return the money
years

Answer 1

Here, principal (starting amount) $=\$1000$
Total amount $=\$1300$

We get the total amount by adding the interest to the principal.
$\because \text{Principal + Simple Interest}=\text{Total Amount}$
$\Rightarrow \text{Simple Interest}=\text{Amount}-\text{Principal}$
$\Rightarrow \text{Simple Interest =}1300-1000$
$\Rightarrow \text{Simple Interest =}300\dots \left(i\right)$

Also, $\text{Simple Interest}=\frac{PRT}{100}\dots \left(ii\right)$
where, P = Principal, R = Rate of interest (expressed in $\%$ per annum) and T = time period (in years)

From $\left(i\right)$ and $\left(ii\right),$ we get
$300=\frac{PRT}{100}$
$\Rightarrow 300=\frac{1000\times 6\times T}{100}$
On simplifying, we get
$300=10\times 6\times T$
$\Rightarrow 300=60\times T$

Dividing both the sides by $60,$ we get
$\frac{300}{60}=T$
Simplify and cancel the common factors, we get
$T=\frac{5\times 60}{60}$
$\Rightarrow T=5$ years

Hence, Jack returned the money after 5 years.