Sample Material of Online Coaching For SSC CGL (Tier - 2) - Compound Interest
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter : Compound Interest)
In compound interest, the interest is added to the principal at the end of each period and the amount thus obtained becomes the principal for the next period. The process is repeated till the end of the specified time.
If P = Principal,
R = Rate per cent per annum
Time = Number of years,
CI = Compound Interest
A = Amount. Then,
When the interest is compounded annually
Important Formulae
1. If the rate of interest differs from year to year ie, R1 in the first year, R2 in the second year, R3 in the third year.
Then
2. When the principal changes every year, we say that the interest is compounded annually. Then,
3. When the principal changes as per every six months, we say that the interest is compounded half yearly or semi-annually. Then,
4. When the principal changes every three months, we say that the interest is compounded quarterly. Then,
5. When the principal changes after every month, we say that the interest is compounded monthly. Then,
6. When the interest is compounded annually but time is in fraction say year.
7. The difference between the simple interest and compound interest for 2 year (or terms) is given by the formula
Where D is the difference, P is the principal and R is the rate of interest.
8. Present worth of x Rs due n years, hence is given by
Example 1: Find compound interest on Rs 12000 for 3 year, if the rate of interest for first year is 5%, second year is 6% and third year is 7%.
Solution: P = Rs 12000, R1 = 5%, R2 = 6% and R3 = 7%
Amount = P(1+R1)(1+R2)(1+R3) 100 100 100
= Rs [12000(1+5 )(1+ 6 )(1+ 7 )] 100 100 100
= Rs [12000x105x106x107] 100 100 100
= Rs 14290.92
Compound interest = Rs (14290.92 – 12000) = Rs 2290.92s
:: Home Assignment for Practice ::
1. The difference between the simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs 124.05. What is the principal sum?
(a) Rs 9000
(b) Rs 8000
(c) Rs 10,000
(d) Rs 13,000
2. The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs 16. If the interest were compounded half-yearly, the difference in two interests would be:
(a) Rs 24.81
(b) Rs 30
(c) Rs 31.61
(d) Rs 35
3. A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs 482 more, if the interest was payable half-yearly than if it was payable annually. The sum is:
(a) Rs 12,000
(b) Rs 20,000
(c) Rs 40,000
(d) Rs 60,000
4. On a sum of money, the simple interest for 2 years is Rs 660, while the compound interest is Rs 696.30, the rate of interest being the same in both the cases. The rate of interest is:
(a) 13%
(b) 14%
(c) 12%
(d) 11%
5. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
(a) 6.10%
(b) 6.11%
(c) 6.08%
(d) 6.09%