Question

A sum of money becomes ? of itself in 5 years at a certain rate of simple interest. The rate per annum is​

Answer 1

Answer:

Let the Initial principle amount =P

After 5 years the amount received =(58)P

As the interest applicable is simple interest, the total interest is Final amount received − Initial principle amount.

Interest amount for 5 years =(58)P−P

Interest amount for 5 years =(53)P

With simple interest, interest amount every year is the same.

Thus interest for one year = Interest for 5 years ÷5

Interest for one year =5(53)P

Interest for one year =253P

Simple Rate of interest per year =Initial Principle amountAmount of Interest received per year ×100%

∴ Rate of interest per year =((253)P÷P)×100%

∴ simple rate of interest =253×100%

∴ Simple Rate of interest =12%

 

Answer 2

Answer:

▩ Given :-

A sum of money becomes double of itself in 5 years in simple interest

Time (t) = 5 years

▩ To Find :-

Rate of simple interest given

▩ Solution :-

Let,

R = Rate of Interest

P = Principal

A = Amount = 2P

Therefore, Simple Interest = Amount - Principal

➸ SI = 2P - P

➸ SI = P

We know that formula for SI is :-

$\boxed{\sf SI = \dfrac{PRT}{100}}$

According to the question,

$\sf →P = \dfrac{P \times R \times 5}{100}$

$\sf →P \times 100 = P \times R \times 5$

$\sf →\dfrac{\cancel{P} \times 100}{\cancel{P}} = R \times 5$

$\sf →100 = R \times 5$

$\sf →R = \dfrac{\cancel{100}}{\cancel{5}}$

$\sf →\fbox \green{R = 20\%}$

Hence the Rate of simple interest per annum is 20%.