Question

A certain sum of money amounts to 5/4 of itself in 5 year. Find the rate percent per annum.

Answer 1

explanation

Let the principal be x, Amount in 5 yrs = 5/4x  

            therefore 

SI = (Amount – Principal) =  5/4x – x = 1/4.x

SI = P × R × T / 100

x/4 = x × R × 5 / 100

 ⇒ R = 5%


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Answer 2

Given :

A certain sum of money amounts to $\dfrac{5}{4}$ of itself in 5 year

To Find :

The rate percentage per annum

Solution :

From compound interest method

Let the rate of interest = r%

Amount = Principal × $(1+\dfrac{rate}{100})^{time}$

Or,  A = P × $(1+\dfrac{r}{100})^{t}$

Or,  $\dfrac{5}{4}$ P = P × $(1+\dfrac{r}{100})^{5}$

or,  $\dfrac{5}{4}$ =  $(1+\dfrac{r}{100})^{5}$

Taking power $\dfrac{1}{5}$ both side

i.e   $( \dfrac{5}{4})^{\dfrac{1}{5}}$  =  $((1+\dfrac{r}{100})^{5})^{\dfrac{1}{5} }$

Or,  1.04 = $(1+\dfrac{r}{100})$

Or,   $\dfrac{r}{100}$ = 1.04 - 1

i.e  $\dfrac{r}{100}$ = .04

∴    rate = 4 %

Hence, The rate of interest per annum is 4%  Answer