Revision Notes on Compound Interest
Compounded Interest
Interest is the extra money paid by the banks on our money at a fixed rate of interest.
Where P = Principal amount
R = Rate of interest
T = Time period for which the interest is paid
The interest calculated both on the principal and the interest earned is called compounded interest.
Example
A sum of Rs. 20,000 is invested by Honey for 2 years at an interest of 8% compounded annually. Find the Compound Interest (C.I.) and the amount she has to pay at the end of 2 years.
Solution:
Step 1 Firstly calculate the Simple Interest (S.I.) for one year.
Let the principal for the first year be P1. Here, P1 = Rs.20, 000
SI1 = SI at 8% p.a. for 1st year = (20000 × 8)/100 = 1600 Rs.
Step 2: now find the principal for the next year
Amount at the end of 1st year = P1 + SI1 = Rs. 20000 + Rs. 1600 = Rs. 21600 = P2 (Principal for 2nd year)
Step 3: Now the new principal for another year = 21600 Rs.
SI2 = SI at 8% p.a. for 2nd year
Amount at the end of 2nd year = P2 + SI2 = Rs. 21600 + Rs.1728 = Rs. 23328
The Formula for Amount
The Formula for Compound Interest
Compound Interest (CI) = Amount (A) – Principal (P)
Example
If a person borrow Rs 15,000 for 3 years at an interest rate of 10% compounded annually. Then what will be Compound Interest and the amount to be paid by him?
Solution:
Given,
P = 15000, r = 10%, n = 3
= 19965 Rs.
CI = A – P
= 19965 – 15000
= 4965 Rs.
The Formula for the Rate Compounded Half Yearly
Case-1 When interest as compounded annually but rate are different for different years.
Case-2. When interest decrease like depreciation in the value of machines
Case-3. Rate Compounded Half Yearly (Semi-Annually)
Case-4. Rate Compounded Quarterly
time period (n) = triplet, rate = quarter
Applications of Compound Interest Formula
There are so many practical situations where the concept of compound interest is used.