Question

3. A certain sum of money at simple interest amounts to $560 in 3 years and to
$600 in 5 years. Find the principal and the rate of interest. [Ans. $ 500; 4%]​

Answer 1

Answer: principal value = $500 and rate of interest = 4%.

Step-by-step explanation:

Let P = Principal value, r= rate of interest, t= time.

Formula for simple interest:

Interest = P x r x t

Final amount = P+ interest

= P+Prt

= P(1+rt)

Simple interest amounts to $560 in 3 years.

⇒ 560=  P(1+3r)

$\Rightarrow\ P=\dfrac{560}{1+3r}$                   (i)

Simple interest amounts to $600 in 5 years.

⇒ 600=  P(1+5r)

$\Rightarrow\ P=\dfrac{600}{1+5r}$                   (ii)

From (i) and (ii) , we get

$\dfrac{560}{1+3r}=\dfrac{600}{1+5r}\\\\\Rightarrow\ 560(1+5r)=600(1+3)\\\\\Rightarrow\ 560+2800r=600+1800r\\\\\Rightarrow\ 2800r-1800r=600-560\\\\\Rightarrow\ 1000r=40\\\\\Rightarrow\ r=\dfrac{40}{1000}\\\\\Rightarrow\ r= 0.04= 4\%$

Put r= 0.04 in (ii), we get

$P=\dfrac{600}{1+5(0.04)}\\\\=\dfrac{600}{1+0.2}\\\\=\dfrac{600}{1.2}\\\\=500$

Hence, principal value = $500 and rate of interest = 4%.