Question

A sum of money becomes double of itself in 5 years at a certain rate of interest. Find the rate of simple
interest per annum.​

Answer 1

Given -:

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

Assume that -:

Rate of interest = R

Principal = P

Amount , A = 2P

Hence, Simple interest = Amount - Prinicpal

= SI = 2P - P

SI = P

Time n = 5 Years.

According to the question -:

SI =

$\bf\frac{p \times r \times n}{100}$

$\bf \: p = { \frac{p \times r \times 5}{100} }$

100 × P = P × R × 5

P × R × 5 = 100 × 5

$\bf r \times 5 = \frac {100 \times p}{p}$

R × 5 = 100

R = 100/5

R = 20

Rate of interest = 20%...

Answer 2

▩ 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,

1. R = Rate of Interest
2. P = Principal
3. 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%.