A sum of money with compound interest becomes Rs. 400 in 2 years and Rs.500 in 3 years. Find the sum
Answers
Answer: 256
Step-by-step explanation: Compound interest= A – P= 500 – 400= 100
Interest = P x R x T/100
100 = 400 x R x 1/100
R = 100 x 100/400 = 25%
A = P {1+R/100}n
400 = P {1+25/100}2
400 = P {5/4}2
400 = 25P/16
P = 400 x 16/25 = 16 x 16 = 256
The sum is Rs. 256
Given: A sum of money with compound interest becomes Rs. 400 in 2 years and Rs.500 in 3 years.
To Find: The sum.
Solution:
- We can find the interest earned for 1 year, by subtracting the amount received for 3 years and 2 years.
- Since, it is just for 1 year, it does not matter whether we use the formula of simple interest or compound interest to find the rate of interest.
- We know that the formula of compound interest is given by the formula,
Amount = P ( 1 + R/100 )^n
where P = Principle amount, R = rate, n = time
According to the numerical,
Interest for 1 year = Rs. ( 500 - 400 )
= Rs. 100
Now, for finding the rate of interest, we shall use the formula of simple interest which is given by,
Interest (I) = ( Principle (P) × Rate (R) × Time (T) ) / 100
Where P = Rs. 400, I = Rs. 100, T = 1 year
Putting respective values in the formula, we get;
Interest (I) = ( Principle (P) × Rate (R) × Time (T) ) / 100
⇒ 100 = ( 400 × R × 1 ) / 100
⇒ R = 100/4
= 25 %
Now, let the original sum be 'X'
As said earlier the formula of compound interest is,
Amount = X ( 1 + R/100 )^n
where, amount = Rs. 400, R = 25%, n = 2 years.
Putting the respective values in the formula, we get;
⇒ 400 = X ( 1 + 25/100 )²
⇒ 400 = X × (5/4)²
⇒ X = 400 × (4/5)²
= Rs. 256
Hence, the sum is Rs. 256.
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