Complete the table and convert tabular data into graphical representation
Simple Interest Compound Interest
Initial deposit Rs.5000,R=10% Rs.5000 ,R=10%
after 1 year
after 2 years
after 3 years
after 4 years
after 5 years
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Answers
Answer:
Dividing both equations, we get
[1 + (R/100)]3 = 1003.50 / 669 = 1.50
Now, we put this value in the equation P [1 + (R/100)]3= 669
=> P x 1.50 = 669
=> P = 446
Thus, the required sum of money is Rs. 446
Question 6 : An investment doubles itself in 15 years if the interest is compounded annually. How many years will it take to become 8 times?
Solution : it is given that the investment Dividing both equations, we get
[1 + (R/100)]3 = 1003.50 / 669 = 1.50
Now, we put this value in the equation P [1 + (R/100)]3= 669
=> P x 1.50 = 669
=> P = 446
Thus, the required sum of money is Rs. 446
Question 6 : An investment doubles itself in 15 years if the interest is compounded annually. How many years will it take to become 8 times?
Solution : it is given that the investmentThe amount which is lent / deposited is called Principal
The money that the principal generates is called Interest. This is the money generated as a result of borrowing/lending.
Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only.
Amount, A = P [1 + (R / 100)]n, where P is the principal, R is the rate of interest per unit time period and n is the time period.
Compound Interest, CI = Amount – Principal
If compounding period is not annual, rate of interest is divided in accordance with the compounding period. For example, if interest is compounded half yearly, then rate of interest would be R / 2, where ‘R’ is the annual rate of interest.
If interest is compounded daily, rate of interest = R / 365 and A = P [ 1 + ( {R / 365} / 100 ) ]T, where ‘T’ is the time period. For example, if we have to calculate the interest for 1 year, then T = 365. For 2 years, T = 730.
If interest is compounded monthly, rate of interest = R / 12 and A = P [ 1 + ( {R / 12} / 100 ) ]T, where ‘T’ is the time period. For example, if we have to calculate the interest for 1 year, then T = 12. For 2 years, T = 24.
If interest is compounded half yearly, rate of interest = R / 2 and A = P [ 1 + ( {R / 2} / 100 ) ]T, where ‘T’ is the time period. For example, if we have to calculate the interest for 1 year, then T = 2. For 2 years, T = 4.
For finding the time period in which a sum of money will double itself at R % rate of compound interest compounded annually, we generally use either of the following two formulas :
Time, T = 72 / R Years
Time, T = 0.35 + (69 / R) Years
When rate of interest is different for different years, say R1, R2, R3 and so on, the amount is calculated as A = P [1 + (R1 / 100)] [1 + (R2 / 100)] [1 + (R3 / 100)] …
Sample Problems
Question 1 : Find the compound interest on Rs. 10,000 at 10% per annum for a time period of three and a half years.
Solution : Time period of 3 years and 6 months means for 3 years, the interest is compounded yearly and for the remaining 6 months, the interest is compounded compounded half yearly. This means that we have 3 cycles of interest compounded yearly and 1 cycle of interest compounded half yearly.
So, Amount = P [1 + (R / 100)]3 [1 + ( {R/2} / 100 )]
=> Amount = 10000 [1 + 0.1]3 [1 + 0.05]
=> Amount = 10000 (1.1)3 (1.05)
=> Amount = Rs. 13975.50
=> Compound Interest, CI = Amount – Principal = 13975.50 – 10000
Therefore, CI = Rs. 3975.50
Question 2 : If Rs. 5000 amounts to Rs. 5832 in two years compounded annually, find the rate of interest per annum.
Solution : Here, P = 5000, A = 5832, n = 2
A = P [1 + (R / 100)]n
=> 5832 = 5000 [1 + (R / 100)]2
=> [1 + (R / 100)]2 = 5832 / 5000
=> [1 + (R / 100)]2 = 11664 / 10000
=> [1 + (R / 100)] = 108 / 100
=> R / 100 = 8 / 100
=> R = 8 %Complete the table and convert tabular data into graphical representation
Simple Interest Compound Interest
Initial deposit Rs.5000,R=10% Rs.5000 ,R=10%
after 1 year
after 2 years
after 3 years
after 4 years
after 5 years
FIND THE MEDIAN OF:
II
25,18,13,20,16,9,22,8,6,15,21,11,17Definition of reproduction
1: the act or process of reproducing
specifically : the process by which plants and animals give rise to offspring and which fundamentally consists of the segregation of a portion of the parental body by a sexual or an asexual process and its subsequent growth and differentiation into a new individual