Question

In what time will $\$2500$ lent at 2% per annum on simple interest earn as much interest as $\$3000$ will earn in 5 years at 5% per annum on simple interest?

• A. $25$ years
• B. $5$ years
• C. $10$ years
• D. $15$ years

Answer 1

The correct option is D $15$ years

$\text{Given,}{P}_1\text{= Principal}=\$2500$
$R_1\text{= Rate of interest}=2\%$
Let time period be $T_1$
$\therefore {\text{Simple Interest}}_1=\frac{PRT}{100}=\frac{2500\times 2\times T_1}{100}$

and $P_2\text{= Principal}=\$3000$
$R_2\text{= Rate of interest}=5\%$
$T_2\text{= Time period = 5 years}$
$\therefore {\text{Simple Interest}}_2=\frac{PRT}{100}=\frac{3000\times 5\times 5}{100}$

According to question,
${\text{Simple Interest}}_1={\text{Simple Interest}}_2$
$\Rightarrow \frac{2500\times 2\times T_1}{100}=\frac{3000\times 5\times 5}{100}$
$\Rightarrow \frac{25\times 100\times 2\times T_1}{100}=\frac{30\times 100\times 5\times 5}{100}$

Cancel out common factors, we get
$\Rightarrow 25\times 2\times T_1=30\times 5\times 5$
$\Rightarrow 50\times T_1=150\times 5$
$\Rightarrow 50\times T_1=750$

Dividing both the sides by $50,$ we get
$T_1=\frac{750}{50}$

Simplify and cancel out common factors, we get

$\Rightarrow T_1=\frac{15\times 50}{50}$
$\Rightarrow T_1=15$

Hence, required time period is $15$ years.