Question

A certain sum amounts to 3798.60 after 3 years and 3878.46 after 4 years. Find the
interest rate and the sum.​

Answer 1

Answer:

comment me if my answer is correct and

Answer 2

Basic Concept Used :-

Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.

Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.

Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.

Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.

Amount = Principal + Simple Interest

and simple interest is same every year.

Let's solve the problem now!!

Let

• Principal be Rs P

• Rate of interest be R % per annum

and

• Simple interest be Rs I

It is given that,

A certain sum of Rs P amount in 3 years to Rs 3798.60

$\rm :\longmapsto\:P + 3I = 3798.60 - - - (1)$

and

A certain sum of Rs P amount in 4 years to Rs 3878.46

$\rm :\longmapsto\:P + 4I = 3878.46 - - - (2)$

On Subtracting, equation (1) from equation (2), we get

$\bf\implies \:I \: = \: 79.86 - - - (3)$

On substituting the value of I, in equation (1), we get

$\rm :\longmapsto\:P + 3 \times 79.86 = 3798.60$

$\rm :\longmapsto\:P + 239.58 = 3798.60$

$\bf\implies \:P \: = \: 3559.02$

Now,

We know that,

$\rm :\longmapsto\:Rate = \dfrac{I \times 100}{P \times \: T }$

where,

• P is the Principal = Rs 3559.02

• T is time period = 1 year

• I is Simple interest on 1 year = Rs 79.86

On substituting all these values in above formula, we get

$\rm :\longmapsto\:Rate = \dfrac{79.86 \times 100}{3559.02 \times 1}$

$\bf\implies \:Rate \: = \: 2.24 \: \% \: approx.$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{Principal = Rs \: 3559.02} \\ &\sf{Rate \: of \: interest = 2.24\% \: per \: annum} \end{cases}\end{gathered}\end{gathered}$

Additional Information :-

$\: \: \: \: \boxed{ \rm \: I = \dfrac{P \times R \times T}{100}}$

$\: \: \: \boxed{ \rm\: T = \dfrac{I \times 100}{P \times R} }$

$\: \: \: \boxed{ \rm \: P = \dfrac{I \times 100}{R \times T}}$