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%]

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)

                  (i)

Simple interest amounts to $600 in 5 years.

⇒ 600=  P(1+5r)

                  (ii)

From (i) and (ii) , we get

Put r= 0.04 in (ii), we get

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

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step-by-step explanation:

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