Compound Interest is the interest calculated on the initial principal and the accumulated interest of previous periods of a deposit or loan.
In easy words, it can be said as "interest on interest". It makes a deposit or loan grow faster as compared to simple interest. The interest at which compound interest accumulates depends on the frequency of compounding; more the number of compounding periods, the greater the compound interest.
Note: The interest for the first month is same in both Simple Interest and Compound Interest. From second month, the interest starts changing.
The formula for Compound Amount
P [1+ R/100]n [When money is compounded annually]
= P [1+ R/(2*100)]2n [When money is compounded half-yearly]
= P [1+ R/(12*100)]12n [When money is compounded monthly]
Also, A = CI + P
Where,
P= Principal
R= Rate of Interest
n=Time (in years)
A= Amount
CI= Compound Interest
Note: The above formula: A = CI + P will give us total amount. To get the Compound Interest only, we need to subtract the Principal from the Amount.
The table given below lists the values of an initial investment, P = Re. 1 for certain time periods and rates of interest, calculated at both, simple and compound interest. If memorized this would be of great help in time management during the exam,
To understand the above discussed concepts, let's try some questions.
Solved Questions
Questions 1:Find the amount if £ 20000 is invested at 10% p.a. for 3 years.
Solution: Using the formula:A= P [1+ R/100]n
A = 20000 [1 + (10/100)]3
On Solving, we get A = £ 26620
Question 2: Find the CI, if £ 1000 was invested for 1.5 years at 20% p.a. compounded half yearly.
Solution: As it is said that the interest is compounded half yearly. So, the rate of interest will be halved and time will be doubled.
CI = P [1+(R/100)]n – P
CI = 1000 [1+(10/100)]3- 1000
On Solving, we get
CI = £. 331
Question 3: The CI on a sum of £ 625 in 2 years is £ 51. Find the rate of interest.
Solution: We know that A = CI + P
A = 625 + 51 = 676
Now going by the formula: A = P [1+(R/100)]n
676 = 625 [1+(R/100)]2
676/625 = [1+(R/100)]2
We can see that 676 is the square of 26 and 625 is the square of 25
Therefore, (26/25)2 = [1+(R/100)]2
26/25 = [1+(R/100)]
26/25 - 1 = R/100
On solving, R = 4%
Question 4:A sum of money is put on CI for 2 years at 20%. It would fetch £ 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.
Solution: Let the Principal = £ 100
When compounded annually,
A = 100 [1+20/100]2
When compounded half yearly,
A = 100[1+10/100]4
Difference, 146.41 - 144 = 2.41
If difference is 2.41, then Principal = £ 100
If difference is 482, then Principal = 100/2.41 × 482
P = £ 20000.
Question 5: Manish invested a sum of money at CI. It amounted to £ 2420 in 2 years and £ 2662 in 3 years. Find the rate percent per annum.
Solution: Last year interest = 2662 - 2420 = £ 242
Therefore, Rate% = (242 * 100)/(2420 * 1)
R% = 10%
Important Formula: To find the difference between SI and CI for 2 years, we use the formula Difference = P[R/100]2
Question 6:The difference between SI and CI for 2 years @ 20% per annum is £ 8. What is the principal?
Solution: Using the formula: Difference = P (R/100)2
8 = P[20/100]2
On Solving, P = £ 200