Question

14. Find difference between simple interest and compound interest on a principal of Rs.5000 for 2 years at the interest rate of 12% p.a., compounded annually.

Answer 1

Answer:

→ Rate of interest is approximately 17.9% .

Answer 2

Step-by-step explanation:

Given:-

• Principal (P) = Rs.5000

• Rate (r) = 12%

• Time (n) = 2 years

To Find:-

• The difference between simple Interest and Compound Interest compounded annually.

Solution:-

$\sf Simple\: Interest = \dfrac{P \times T \times R}{100}$

$\sf \implies SI = \dfrac{5000\times 2 \times 12}{100}$

$\sf \implies SI = 50\times 2 \times 12$

$\sf \implies SI = 1200$

$\sf \therefore \underline{ \: \: \underline{ \: Simple \: Interest = Rs.1200\:}\: \: }$

$\sf Compound \: Interest = Amount - Principal$

$\sf \implies CI = \Bigg[P \bigg(1+\dfrac{r}{100}\bigg)^n\Bigg] - P$

$\sf \implies CI = \Bigg[5000\bigg(1+\dfrac{12}{100}\bigg)^2\Bigg] - 5000$

$\sf \implies CI = \Bigg[5000\bigg(\dfrac{112}{100}\bigg)^2\Bigg] - 5000$

$\sf \implies CI = \Bigg[5000\times\dfrac{12544}{10000}\Bigg] - 5000$

$\sf \implies CI = \bigg(\dfrac{12544}{2}\bigg) - 5000$

$\sf \implies CI = 6272- 5000$

$\sf \implies CI = 1272$

$\sf \therefore \underline{ \: \: \underline{ \: Compound \: Interest = Rs.1272\:}\: \: }$

Now, the difference between Compound Interest and Simple Interest

= CI - SI

= 1272 - 1200

= 72

Therefore:-

The difference between Compound Interest and Simple Interest is Rs. 72