Question

A sum under compound interest, interest being compounded annually amounts to RS.6000 in two years and RS.7200 in three years. Find the rate of interest.
A) 10% B) 20% C) 18% D) 15%

[Answer: B; please provide the step by step explainition]
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Answer 1

$\huge\underline{\sf{Solution-}}$

Let

• Sum invested be Rs P

and

• Rate of interest be R % per annum

We know that,

• Amount (A) on certain sum of money P invested at the rate of R % per annum compounded annually for 'n' years is

$\rm :\longmapsto\:A = P {\bigg(1 + \dfrac{R}{100}\bigg) }^{n}$

According to statement,

• A sum of money P amounts to Rs 6000 in 2 years at the rate of R % per annum.

So,

$\rm :\longmapsto\:6000 = P {\bigg(1 + \dfrac{R}{100} \bigg) }^{2} - - - (1)$

Also,

• A sum of money P amounts to Rs 7200 in 3 years at the rate of R % per annum.

$\rm :\longmapsto\:7200 = P {\bigg(1 + \dfrac{R}{100} \bigg) }^{3} - - - (2)$

• On dividing equation (2) by equation (1), we get

$\rm :\longmapsto\:\dfrac{7200}{6000} = \dfrac{P {\bigg(1 + \dfrac{R}{100} \bigg) }^{3}}{P {\bigg(1 + \dfrac{R}{100} \bigg) }^{2}}$

$\rm :\longmapsto\:\dfrac{6}{5} =1 + \dfrac{R}{100}$

$\rm :\longmapsto\:\dfrac{6}{5} - 1 = \dfrac{R}{100}$

$\rm :\longmapsto\:\dfrac{6 - 5}{5} = \dfrac{R}{100}$

$\rm :\longmapsto\:\dfrac{1}{5} = \dfrac{R}{100}$

$\rm :\implies\:R \: = \: 20 \: \%$

${\boxed{\boxed{\bf{Option \: (B) \: is \: correct}}}}$

Additional Information :-

1. Amount (A) on certain sum of money P invested at the rate of R % per annum compounded half yearly for 'n' years is

$\rm :\longmapsto\:A = P {\bigg(1 + \dfrac{R}{200} \bigg) }^{2n}$

2. Amount (A) on certain sum of money P invested at the rate of R % per annum compounded quarterly for 'n' years is

$\rm :\longmapsto\:A = P {\bigg(1 + \dfrac{R}{400} \bigg) }^{4n}$

3. Amount (A) on certain sum of money P invested at the rate of R % per annum compounded monthly for 'n' years is

$\rm :\longmapsto\:A = P {\bigg(1 + \dfrac{R}{1200} \bigg) }^{12n}$

Answer 2

Answer:

The Rate of interest will be 20%

Step-by-step explanation:

The concept of compound interest

Amount= 6000 in two years

7200 in three Years

Amount= P×(1+R/100)*n

P is principal

R is rate of interest

n is no of years

Now,

P× (1+R/100)*2= 6000 ------(1)

P×(1+R/100) *3= 7200 ------(2)

Now, divide equation 2 By 1 we get

1+R/100 = 1.2

R= 20% which is required answered