Question

Q Calculate compound interest and simple interest if P=Rs.2000 , R=10\% p.a,Time=2 years. Which interest is cheaper. If you are a money lender which interest yo u will charge to customer? Explain. ​

Answer 1

Answer:

Simple interest is cheaper.

Explanation:

Given,

• P(principal) = ₹2,000
• R(rate) = 10%
• T(time) = 2 years.

Calculating Compound interest :-

$\rm \longrightarrow C. I. = Amount - Principal$

• Amount formula :- $\rm p\bigg(1 + \dfrac{r}{100}\bigg)^n$

Then,

$\rm \longrightarrow \: 2000\bigg(1 + \dfrac{10}{100}\bigg)^2$

$\rm \longrightarrow \: 2000\bigg(1 + \dfrac{1}{10}\bigg)^2$

$\rm \longrightarrow \: 2000\bigg(\dfrac{11}{10}\bigg)^2$

$\rm \longrightarrow \: 2000\bigg(\dfrac{121}{100}\bigg)$

$\rm \longrightarrow \: 20 \cancel{00}\bigg(\dfrac{121}{ 1\cancel{00}}\bigg)$

$\rm \longrightarrow \: 20 \times 121$

$\rm \longrightarrow \: 2420$

Then, compound interest is :-

$\rm \longrightarrow C. I. = Amount - Principal$

$\rm \longrightarrow C. I. = 2420 - 2000$

$\rm \longrightarrow C. I. = 420$

$\rm \therefore C. I. = 420$

Calculating simple interest :-

$\rm \longrightarrow S. I. = \dfrac{p \times r \times t}{100}$

$\rm \longrightarrow \dfrac{20 \cancel{00} \times 10\times 2}{1 \cancel{00} }$

$\rm \longrightarrow 400$

$\rm \therefore \: S. I. \: = 400$

Clearly,

= C. I. > S. I.

Hence, simple interest is cheaper. So I would prefer to charge at simple interest for easy deal.

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Formula used :

• $\rm C. I. = Amount - Principal$
• Amount formula :- $\rm p\bigg(1 + \dfrac{r}{100}\bigg)^n$
• $\rm S. I. = \dfrac{p \times r \times t}{100}$

Here, p denotes the principal, r is the rate and t is the time.