The difference between compound interest and simple interest on a certain principal for two years at 20% rate of interest is Rs. 25. What is the Principal amount ? (Answer with theory)
let the principal be P
simple interest:
amount = P + .2P(2) = P(1 + .4) or 1.4P
compound interest amount = P(1.2)^2
P(1.2)^2 - 1.4P = 25
solve for P
To find the principal amount, we need to understand the difference between compound interest and simple interest.
Simple Interest:
Simple interest is calculated only on the initial principal amount. It does not take into account any interest that accrues over time. The formula to calculate simple interest is:
Simple Interest = (Principal) x (Rate) x (Time)
Compound Interest:
Compound interest is calculated on both the initial principal amount and the interest that accumulates over time. The interest is added to the principal amount at regular intervals, resulting in higher returns. The formula to calculate compound interest is:
Compound Interest = Principal x [1 + (Rate/100)]^Time - Principal
Now, let's solve the given problem:
Given:
Rate of interest = 20%
Difference between compound interest and simple interest = Rs. 25
Time = 2 years
Let's assume the principal amount as P.
First, we will calculate the compound interest using the compound interest formula:
Compound Interest = P x [1 + (Rate/100)]^Time - P
= P x [1 + (20/100)]^2 - P
= P x (1.2)^2 - P
= P x 1.44 - P
= 1.44P - P
= 0.44P
Next, we will calculate the simple interest using the simple interest formula:
Simple Interest = P x Rate x Time
= P x 20/100 x 2
= 0.4P
Given that the difference between compound interest and simple interest is Rs. 25, we can set up the equation:
Compound Interest - Simple Interest = 25
0.44P - 0.4P = 25
0.04P = 25
P = 25 / 0.04
P = Rs. 625
Therefore, the principal amount is Rs. 625.