Question
A person invests Rs10000 for two years at a certain rate of interest compounded annually. At the end of one year, the sum amounts to Rs12000. Calculate (i). the rate of interest per annum (ii) the amount at the end of the second year
Use simple interest to find the rate of interest and from that find total amount at the end of 2years.
The correct answer is: 14400 RUPEES
Complete step by step solution:
(i)
We know the formula for total amount = A = P +
SI…(i)
where A is the total amount, P is the principal amount and SI is simple interest.
(for 1st year, both simple interest and compound interest are the same)
Here, we have A = 12000 Rs and P = 10000 Rs
On substituting the known values in (i), we get SI = 12000 - 10000 = 2000
So, we have SI = 2000 Rs
We calculate simple interest by the formula,…(ii)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have SI = 2000, P = 10000,T = 1 and R
= ?
On substituting the known values in (ii), we get Hence the rate of interest R is 20%.
(ii)
We know that …(iii)
Here, we have T = 2 years, P = 10000 , R = 20%
Amount at the end of second year will be,
On substituting the known values in (iii), we get
Rupees
(ii)
We know that …(iii)
Here, we have T = 2 years, P = 10000 , R = 20%
Amount at the end of second year will be,
On substituting the known values in (iii), we get
Book A Free Demo
Mobile*
I agree to get WhatsApp notifications & Marketing updates
Related Questions to study
>
At what rate per cent per annum compound interest will Rs. 4000 amount to Rs. 5324 in 3 years
Solution
Given that principal,p = Rs.4000
Amount, A = Rs. 5324
let the rate of interest = r%.
Given time,n = 3 years.
Then from equation of compound interest, we know
A = p×(1 + r/100)n
5324 = 4000(1 + r/100)3
5324/4000 = (1 + r/100)3
1331/1000 = (1 + r/100)3 [ cube root on both sides]
(11 / 10)3 = (1 + r/100)3
11 / 10 = 1 + r / 100
(11 / 10)-1 = r / 100.
1 / 10 = r / 100
r = 100/10
∴ r =10%.
Hence the rate of interest is 10%.
Suggest Corrections9
In what time will Rs. $ 4000 $ amount to Rs. $ 5,324 $ at $ 10\% $ p.a. in CI?
A. $ 1 $ years
B. $ 2 $ years
C. $ 3 $ years
D. $ 4 $ years
Answer
Verified
Hint: Here, C.I. stands for compound interest in which interest on interest which was accumulated last year is also considered. Interest can be defined as the monetary charge for the privilege for borrowing someone else’s money. Here we will use the standard formula and place the given data and find the required term simplifying the equation.
Complete step-by-step answer:
Given that: Amount, A $ = 5324 $ Rs.
Principal, $ P = 4000 $ Rs.
Rate of interest, $ r
= 10\% $
Here we will use the formula for the compound interest which is given by –
$ A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} $
Place the given values in the above equation –
$ 5324 = 4000{\left( {1 + \dfrac{{10}}{{100}}} \right)^n} $
Remove common factors from the numerator and the denominator and simplify the fraction first in the above expression –
$ 5324 = 4000{\left( {1 + \dfrac{1}{{10}}} \right)^n} $
Take LCM (least common multiple) for the
above expression –
$ 5324 = 4000{\left( {\dfrac{{11}}{{10}}} \right)^n} $
The above expression can be re-written as –
$ 5324 = 4000{\left( {1.1} \right)^n} $
Make the required term the subject and move other terms on the opposite side. Term multiplicative on one side is moved to the opposite side then it goes to the denominator and vice-versa.
$ {\left( {1.1} \right)^n} = \dfrac{{5324}}{{4000}} $
Simplify the above expression considering that common factors
from the numerator and the denominator cancel each other if possible or divide it.
$ {\left( {1.1} \right)^n} = 1.331 $
We know that the $ {11^3} = 1331 $ and so above expression can be re-written as –
$ {\left( {1.1} \right)^n} = {\left( {1.1} \right)^3} $
When bases are the same, powers are equal.
$ \Rightarrow n = 3 $ years
From the given multiple choices – the option C is the correct answer.
So, the correct answer is “Option C”.
Note: Always know the difference between the simple and compound interest and know its standard formula as it is the main and important equation for the correct formula. Amount can be defined as the value which is the sum of the principal value and the interest occurred during the term period.