Question

please guys tell the answer fast
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Answer 1

Question:

Find the difference between compound interest and simple interest on Rs. 12,000 and in $1\frac{1}{2}$ years at 10% p.a.(per annum) compounded yearly.

Solution:

Principal(P) = Rs. 12,000

Rate(r) = 10% per annum

Time(t) = $1\frac{1}{2}$ years = $\frac{3}{2}$ years = 1.5 years

Simple Interest=>

A = P (1 + rt)

A = final amount

P = initial principal balance

r = annual interest rate

t = time (in years)

$A = P (1 + rt)$

$A = 12000 (1 + \frac{10}{100} * \frac{3}{2})$

$A = 12000(1 + \frac{30}{200} )$

$A = 12000(\frac{200 + 30}{200} )$

$A = 12000 * \frac{230}{200}$

$A = 60 * 230$

$A = 13800$

Compound Interest=>

$A = P(1 + \frac{r}{n})^{nt}$

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

$A = P(1 + \frac{r}{n})^{nt}$

$A = 12000(1 + \frac{10}{1*100})^{1 * 1.5}$

$A = 12000(1 + 0.1)^{1 * 1.5}$

$A = 12000 * 1.1^{1.5}$

$A = 12000 * 1.15369$

$A = 13844.28$

The amount after applying simple interest after 1.5 years is Rs.13800

Interest applied Amount = A - P = 13800 - 12000 = Rs. 1800

The amount after applying compound simple interest after 1.5 years is Rs.13844.28

Compound Interest applied Amount = A - P = 13844.28 - 12000 = Rs.1844.28

In the question it is asked to take out difference between compound interest and simple interest

Difference between compound and simple interest = 13844.28 - 13800 = Rs. 44.28

The difference between compound and simple interest is Rs. 44.28

Answer 2

Given : Amount 12000  & time period 1 1/2 years and Rate of interest = 10 % per annum , Compounded annually

To find : Difference between Simple & Compound interest

Solution:

Principle amount P  = Rs 12000

Rate of interest = 10 % per annum

Simple interest = P * R * T / 100

Simple interest in  1 1/2 years   = 12000 * 10 * (3/2) / 100 = Rs 1800

Interest for 1st Year = 12000 * 10 * 1 /100 = Rs 1200

Principle amount after 1 year 12000 + 1200 = Rs 13200

Interest for next 6 months =  13200 * 10 *(1/2) / 100  = Rs660

Total Compound interest =  1200 + 660  = Rs 1860

Difference in Compound & simple interest = 1860 - 1800 = Rs 60

or Simple way  Difference in simple interest & compound  interest will be interest earned in 6 months on interest earned in 1st years at simple interest rate

interest in 1st year = Rs 1200

interest in next 6 months on rs 1200   =   1200 * 10 (1/2) /100 = Rs 60

Hence Difference between compound & simple interest = Rs 60

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