Simple Interest and Compound Interest
Interest (I): The additional amount paid by the borrower to the lender for the use of a sum of money.
Principal (P): The sum of money lent, borrowed or invested.
Time (T): The duration for which the sum of money is lent or invested, usually in years.
Rate (R): The interest paid on Rs. 100 per unit of time, usually per annum (p.a.).
Amount (A): The sum of principal and the interest.
Simple Interest: The interest paid on the original sum of money borrowed or invested.
When we say, interest, it always means simple interest.
Compound Interest: Money is said to be lent at compound interest, when the interest, which has become due at the end of a certain fixed period (one year, half year, etc., as given), is not paid to the money lender , but is added to the sum lent. The amount thus obtained becomes the principal for the next period. This process is repeated until the amount for the last period is found.
The difference between the final amount and the original principal is the required compound interest i.e.
Compound Interest = Final Amount – Original Principal
The formula for finding the amount is
Where A = amount
P = principal
r = rate of interest compounded yearly
t = numbers of years
When the rate for successive years are different, then
Where r1 %, r2%, r3% …………………. are the rates for successive years.
Some Important Formulas
- The difference between compound interest and simple interest for some amount of money in 2 years is =
- When the interest is compounded half yearly and rate of interest annually, then the amount will be after t years,
- When the interest is compounded yearly and time is 11 2 years, then amount will
- The compound interest for 2 years in terms of interest is,
- The compound interest for 3 years in terms of simple interest is,
WORKED OUT Questions
- A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months . The rate of interest per annum is
- What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?
Subtracting (1) from (2)
- What should be the least number of years in which the simple interest on Rs. 2600 at 2% will be an exact number of rupees?
If we multiply by 3 in interest for 1 year, we get the exact number of rupees
Minimum time = 3 years.
- Ratio of the principal and the amount after 1 year is 10 :12 . Then the rate of interest per annum is
Solution : P : A = 10 : 12
P : I = 10 : 2
P / I = 10 / 2
R = 20 %.
- A person invests money in three different schemes for 6 years, 10 years and 12 years at 10 percent,12 percent and 15 percent respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is
Solution : Let the principal be P1,P2 and P3 for 6 , 10 and 12 years respectively,
P1 = 100 * (I/6) * 10
P2 = 100 * (I/10) * 12
P3 = 100 * (I/12) * 15
P1 : P2 : P3 = (1/60) * (1/120) * (1/180)
= 6 : 3 : 2.
- The sum of money that yields a compound interest of Rs. 420 during the second year at 5 % per annum is,
- A man saves Rs. 2000 at the end of each year and invests the money at 5% compound interest. At the end of 3 years he will have,
Solution: He saves 2000 at the end of 1st year
Interest in the second year = (200 * 5 * 1) / 100 = 100
Amount = 2000 + 100 = 2100
He saves another 2000 at the end of 2nd year
Principal for the 3rd year = 2100 + 2000 = 4100
Interest in the 3rd year = (4100 * 5 *1)/100 = 205
Amount = 4100 + 205 = 4305
But he saves 2000 at the end of 3rd year
So total amount = 4305 + 2000 = 6305.
- The difference between the compound interest and simple interest for the amount Rs. 5000 in 2 years is Rs. 32. The rate of interest is,
Solution: Simple interest for 1st year = (5000 * R * 1)/100 = 50R
Simple interest for 2nd year = 50 * R
Compound interest for 2nd year = 50 * R + (50 * R * R)/100
Difference between C.I. and S.I. = 32
- A sum of money doubles itself in 4 years at compound interest. It will amount to 8 times itself at the same rate of interest in
Solution: Let the principal be x
Amount = 2x in 4 years
- If the compound interest on a certain sum for 2 years at 3% per annum is Rs.101.50 , then the simple interest on the same sum at the same rate and for the Same time will be
- An amount of money appreciates to Rs. 7000 after 4 years and to Rs. 10000. After 8 years at a certain compound interest compounded annually. The Initial amount of money was
These notes have been prepared by Plutus Academy.