Question

6. A certain amount of money amounts to 8,600 in 3 years and to 9,800 in 4 years. Find the principe
and rate of interest.​

Answer 1

hope you will understand it

Answer 2

Given:

Amount_1= 8600

Time_1= 3 years

Amount_2= 9800

Time= 4 years

To Find:

The principle and rate of interest.

Solution:

We are going to use the very basis of Simple Interest here which is, Simple interest (S.I) remains the same every year as it's a certain percentage of the Principle.

We know,

Amount= S.I + Principal (P)

S.I= Principal (P)× Rate (r)× Time (t)

Thus using the above-mentioned concept, as we have been given the amounts of two consecutive years, we can consider the amount of the third year (8600) to be the principal and 4th year to be the amount (9800) and get the Simple Interest by finding the difference between them.

⇒Amount= Interest +Principal

⇒9800-8600= Interest

⇒1200 = Interest

As we now know the simple interest the principal yields every year, and that it remains the same, we can find the total simple interest of any year by simply multiplying.

So, for a total span of 4 years, the total Simple interest would be:-

1200×4= 4800 (Total 4 years cumulative S.I)

Now, knowing the amount of the 4th year to be 9800, we can find the original principal.

⇒Amount= Interest +Principal

⇒9800-4800=Principal

⇒5000 = Principal

Thus, as we have the original or starting principal, we can easily find the rate of interest by simply substituting the values in the S.I equation:-

⇒ S.I= Principal (P)× Rate (r)× Time (t)

We are substituting the value of the 4th year,

⇒ 4800= (5000×r×4)÷ 100

⇒ 4800÷(50×4)= rate

⇒ 4800÷200 = rate

⇒ 24% = rate

Hence, the principle is 5000 and the rate of interest is 24%.