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%.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !