Question

the difference between simple interest and compound interest on a certain sum for 2 years at 5% is rupees 500 find the sum​

Answer 1

Step-by-step explanation:

Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."

let time = 2 years

p = 5%

R = 500

p×r×t / 100 = 2×5×500/100

500+ 50 = 550

hope my answer help you

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Time, (n) = 2 years
• Rate, (R) = 5% p.a
• The difference of C.I. & S.I. = 500

$\underline{\bf{Explanation\::}}$

As we know that formula of the compounded annually & Simple Interest;

$\boxed{\bf{Amount = Principal\bigg(1+\frac{R}{100} \bigg)^n}}$

$\boxed{\bf{Simple \:Interest = \frac{PRT}{100}}}$

A/q

Let the sum be r

$\mapsto\tt{A= P\bigg(1+\dfrac{R}{100} \bigg)^{n}}$

$\mapsto\tt{A= r\bigg(1+\dfrac{5}{100} \bigg)^{2}}$

$\mapsto\tt{A= r\bigg(1+\cancel{\dfrac{5}{100}} \bigg)^{2}}$

$\mapsto\tt{A= r\bigg(1+\dfrac{1}{20} \bigg)^{2}}$

$\mapsto\tt{A= r\bigg(\dfrac{20+1}{20} \bigg)^{2}}$

$\mapsto\tt{A= r\bigg(\dfrac{21}{20} \bigg)^{2}}$

Now, as we know that compound Interest;

→ C.I. = Amount - Principal

→ C.I. = Rs.r(21/20)² - Rs.r

________________________________

$\mapsto\tt{S.I. = PRT/100}$

$\mapsto\tt{S.I. = r\times 5 \times 2 /100}$

$\mapsto\tt{S.I. = 1\cancel{0}r /10\cancel{0}}$

$\mapsto\tt{S.I. = r/10}$

Now,

$\longrightarrow\tt{C.I. - S.I. = 500}$

$\longrightarrow\tt{\bigg[r\bigg(\dfrac{21}{20} \bigg)^{2} - r \bigg]- \bigg[\dfrac{r}{10}\bigg] = 500}$

$\longrightarrow\tt{\bigg[r\bigg(\cancel{\dfrac{21}{20}} \bigg)^{2} - r \bigg]- \bigg[\cancel{\dfrac{r}{10}}\bigg] = 500}$

$\longrightarrow\tt{r\times (1.05)^{2} - r - 0.1r = 500}$

$\longrightarrow\tt{ 1.1025r - r - 0.1r = 500}$

$\longrightarrow\tt{ 0.1025r - 0.1r = 500}$

$\longrightarrow\tt{ 0.0025r = 500}$

$\longrightarrow\tt{r = \dfrac{500\times 10000}{0.0025 \times 10000} }$

$\longrightarrow\tt{r = \cancel{\dfrac{5000000}{25} }}$

$\longrightarrow\bf{r = Rs.200000}$

Thus,

The sum will be Rs.200000 .