Question

find the compound interest and the amount for each principal is equal to 8000 rate 5% time 3 years

Answer 1

Answer:

You have learned about the simple interest and formula for calculating simple interest and amount. Now, we shall discuss the concept of compound interest and the method of calculating the compound interest and the amount at the end of a certain specified period. We shall also study the population growth and depreciation of the value of movable and immovable assets.

Step-by-step explanation:

Compound Interest

If the borrower and the lender agree to fix up an interval of time (say, a year or a half year or a quarter of a year etc) so that the amount (Principal + interest) at the end of an interval becomes the principal for the next interval, then the total interest over all the intervals, calculated in this way is called the compound interest and is abbreviated as C.I.

Compound interest at the end of a certain specified period is equal to the difference between the amount at the end of the period and original principal i.e. C.I. = Amount – Principal. In this section, we shall discuss some examples to explain the meaning and the computation of compound interest. Compound interest when interest is compounded annually.

Compound Interest

Example 1

Find the compound interest on Rs 1000 for two years at 4% per annum.

Solution: Principal for the first year =Rs 1000

SI=P×R×T100SIfor1styear=1000×4×1100SIfor1styear=Rs40

Amount at the end of first year =Rs1000 + Rs 40 = Rs 1040. Principal for the second year = Rs1040

SIfor2ndyear=1040×4×1100

SIfor2ndyear=Rs41.60

Amount at the end of second year,  

Amount=Rs1040+Rs41.60=Rs1081.60

Therefore,

Compoundinterest=Rs(1081.60–1000)=Rs81.60

Remark: The compound interest can also be computed by adding the interest for each year.

Compound Interest when Compounded Half Yearly

Example 2: Find the compound interest on Rs 8000 for 3/2 years at 10% per annum, interest is payable half-yearly.

Solution: Rate of interest = 10% per annum = 5% per half –year. Time = 3/2 years = 3 half-years

Original principal = Rs 8000.  

Interestforthefirsthalfyear=8000×5×1100=420

. Amount at the end of the first half-year= Rs 8000 +Rs 400 =Rs8400

Principal for the second half-year =Rs 8400

Interestforthesecondhalf−year=8400×5×1100=420

Amount at the end of the second half year = Rs 8400 +Rs 420 = Rs 8820

Interestforthethirdhalfyear=8820×5×1100=Rs441

Amount at the end of third half year= Rs 8820+ Rs 441= Rs 9261. Therefore, compound interest= Rs 9261- Rs 8000= Rs 1261. Therefore,

compoundinterest=Rs9261−Rs8000=Rs1261

Compound Interest by Using Formula

In this section, we shall obtain some formulae for the compound interest.

Case 1

Let P be the principal and the rate of interest be R% per annum. If the interest is compounded annually, then the amount A and the compound interest C.I. at the end of n years is given by:

A=P(1+R100)n

and

CI=A−PCI=P(1+R100)n−PCI=P[(1+R100)n−1]

Example 3: Find the compound interest on Rs 12000 for 3 years at 10% per annum compounded annually.

Solution: P =Rs 12000, R =10% per annum and n=3. Therefore, amount (A) after 3 years

A=P(1+R100)3A=12000(1+10100)3A=12000(1110)3A=12000(1110)×(1110)×(1110)A=15972Compoundinterest=A−PCI=Rs15972−Rs12000=Rs3972

Case 2

When the interest is compounded half-yearly.

A=P(1+R200)2nCI=P[(1+R200)2n−1]

Case 3

When the interest is compounded quarterly.

A=P(1+R400)4nCI=P[(1+R400)4n−1]

Case 4

Let be the principal and the rate of interest be R1% for the first year, R2% for second year, R3% for third year and so on and last Rn% for the nth year . Then the amount (A) and the compound interest C.I. at the end of n years are given by:  

A=P(1+R1100)(1+R2100)(1+R3100)

A = P (1+R1/100)(1+R2/100)…(1+Rn/100) and

CI=A−P

respectively.

Case 5

Let p is the principal and the rate of interest is R% per annum. If the interest is compounded annually but time is the fraction of a year, say 21/4 years, then amount A is given by:

A=P(1+R100)5(1+R4100)

and

CI=A−P

More Solved Example For You

Example 4: Find the compound interest on Rs 10000 for one year at 20% per annum compounded quarterly.

Solution: Rate of interest = 20% per annum= 20/4%= 5% per quarter. Time = 1 year= 4 quarters

Principal for the first quarter= Rs 10000

Interestforthefirstquarter=10000x5x1100=Rs500

Amount at the end of first quarter =Rs (10000+500) = Rs 10500 , Principal for the second quarter = Rs 10500

Interestforthesecondquarter=10500x5x1100=Rs525

Amount at the end of second quarter= Rs 10500+ Rs 525= Rs 11025. Principal for the third quarter= Rs 11025

Interestforthethirdquarter=11025×5×1100=Rs551.25

Amount at the end of third quarter= Rs11025 + Rs 551.25= Rs 11576.25 . Principal for the fourth quarter= Rs 11576.25

Interestforthefourthquarter=11576.25×5×1100=Rs578.8125

Amount at the end of fourth quarter= Rs 11576.25+ Rs 578.8125= Rs 12155.0625. Therefore, compound interest= Rs 12155.0625- Rs 10000= Rs 2155.625

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Discount and Commission

Answer 2

       $\underline{\bold{Answer:}}$

       $\text{Amount = Rs. 9261, Compound Interest = Rs. 1261}$

       $\underline{\bold{Step-by-step-explaination:}}$

       $\text{Principal}(P) = \text{Rs. 8000}$

       $\text{Rate of Interest}(R) = 5 \text{ o/o}$

       $\text{Time}(T) = 3 \text{ years}$

       $\text{We know that, Amount}(A) = P(1 + \frac{R}{100})^{T}$

$\implies \boxed{A = 8000(1 + \frac{5}{100})^{3} }$

       $\text{Simplifying...}$

$\implies \boxed{A = 8000(1 + \frac{1}{20})^{3} }$

       $\text{Simplifying...}$

$\implies \boxed{A = 8000(\frac{21}{20})^{3} }$

       $\text{Simplifying...}$

$\implies \boxed{A = 8000(\frac{21}{20})(\frac{21}{20})(\frac{21}{20}) }$

       $\text{Simplifying...}$

$\implies \boxed{A =\text{Rs. }9261}$

       $\text{We know that }C.I = A - P$

$\implies \boxed{C.I = 9261 - 8000}$

       $\text{Simplifying...}$

$\implies \boxed{C.I = \text{Rs. }1261}$