At what rate percent per annum compound interest would 8000 amount to 88200

Note:- Before viewing Solutions of Chapter -2 Compound Interest Class-9 of ML Aggarwal Solutions .  Read the Chapter Carefully then solve all example given in Exercise-2.2. The Chapter-2 Compound Interest Class-9 is Main Chapter in Class 9 Mathematics.

Complete step by step answer:-
Compound interest is the interest that is calculated on the principal amount along with the interest accumulated over the previous period or year.
The formula to calculate compound interest with a principal amount P, at an annual rate r for n years is given as follows:
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}............(1)\]
In this problem, the principal amount P is given as Rs. 8000.
\[P = 8000...........(2)\]
The amount is compounded at a rate of 5 % annually.
\[r = 100...........(3)\]
We need to find the number of years n to accumulate an amount of Rs. 8820.
\[A = 8820..........(4)\]
Using equations (2), (3), and (4) in equation (1), we have:
\[8820 = 8000{\left( {1 + \dfrac{5}{{100}}} \right)^n}\]
Simplifying the terms in the bracket we get:
\[8820 = 8000{\left( {1.05} \right)^n}\]
Taking 8000 to the other side and dividing with 8820, we get:
\[\dfrac{{8820}}{{8000}} = {\left( {1.05} \right)^n}\]
\[1.1025 = {\left( {1.05} \right)^n}\]
Apply log to both the sides of the equation, to get as follows:
\[\log (1.1025) = \log ({1.05^n})\]
We know that the value of \[\log {x^n}\] is equal to \[n\log x\].
\[\log (1.1025) = n\log (1.05)\]
We know that the square of 1.05 is 1.1025, then, we have:
\[\log {\left( {1.05} \right)^2} = n\log (1.05)\]
\[2\log \left( {1.05} \right) = n\log (1.05)\]
Solving for n, we have:
\[n = 2\dfrac{{\log (1.05)}}{{\log (1.05)}}\]
\[n = 2\]
Hence, it takes 2 years for the amount Rs. 8000 to change to Rs. 8820 when it is compounded at the rate of 5 % annually.

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.1 in Chapter 2 - Compound InterestCompound Interest (CI)Compound Interest formulaType 1: When the interest is compounded annuallyType 2: When the interest is compounded annually but rates are different for different years.Type 3: When interest is compounded annually but time is a fractionType 4: Interest Compounded Half-YearlyType 5: Interest Compounded QuarterlyAt what rate percent per annum compound interest will Rs 8000 amount to Rs 10648 in three years?At what rate per cent per annum will Rs 8000 amount to Rs 8820 in 2 years at compound interest?At what rate percent per annum compound interest will 8000 amount to 8820 in six months the interest being compounded quarterly?At what rate percent compounded yearly will RS 80000 amounts to Rs 88200 in 2 years?Jump toCompound Interest Exercise 2.1Compound Interest Exercise 2.2Compound Interest Exercise 2.3Rational and Irrational NumbersCompound InterestExpansionsFactorizationSimultaneous Linear EquationsProblems on Simultaneous Linear EquationsQuadratic EquationsIndicesLogarithmsTrianglesMid Point TheoremPythagoras TheoremRectilinear FiguresTheorems on AreaCircleMensurationTrigonometric RatiosTrigonometric Ratios and Standard AnglesCoordinate GeometryStatisticsML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.1 in Chapter 2 - Compound Interest

Question 14 Compound Interest Exercise 2.1

The simple interest on a certain sum of money for 2 years at 10% p.a. is ₹ 1600. Find the amount due

and the compound interest on this sum of money at the same rate after 3 years, interest being reckoned

annually.

Answer:

It is given that

Period = 2 years

Rate = 10% p.a.

We know that

Sum = (SI × 100)/ (r × n)

Substituting the values

= (1600 × 100)/ (10 × 2)

= ₹ 8000

Here

Amount after 3 years = P (1 + r/100)

n

Substituting the values

= 8000 (1 + 10/100)

3

By further calculation

= 8000 × 11/10 × 11/10 × 11/10

= ₹ 10648

So the compound interest = A – P

Substituting the values

= 10648 – 8000

= ₹ 2648

Video transcript

"hey guys welcome to lido q a video i am vinit your lido tutor bringing you this question on your screen the simple interest on a certain sum of money for two years at 10 per annum is rupees 1 600. find the amount due and the compound interest on this sum of money at the same rate after three years so what is given to us simple interest is equal to one thousand six hundred rupees rate of interest is ten percent per annum and time is two years the simple interest is two years we know that simple interest is given by principal into rate into time by 100 this implies 1600 equal to p into 10 into 2 by 100 this implies principle is equal to 1600 into 100 by 20 right therefore principle is equal to rupees 8 000. now i have to find the count interest for this so for compound interest p is equal to rupees 8 000 rate is equal to 10 percent and for 3 years right so t is equal to 3 years therefore amount at the end of 3 year that is the amount u is equal to p into 1 plus r by 100 to the power t this is equal to 8 000 into 1 plus 10 by 100 cube so this is equal to 8 000 into 11 by 10 into 11 by 10 into 11 by 10 right so three zeros cancel out with 10 into 10 into 10 this gives us 11 into 11 into 8 that is equal to rupees 10 648 this is the amount compound interest is amount minus principle minus principle so this is equal to rupees 2648 isn't that easy guys right so if you still have a doubt please leave a comment below do like the video and subscribe to our channel i'll see you in our next video until then bye guys keep learning keep practicing"

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Money is not free to borrow. People can always find a use for money, so it costs to borrow money. Different places charge different amounts at different times! It is called Interest. This lesson explains the concept of Simple Interest and Compound Interest. We will develop a basic understanding of these two different types of interests, their uses and properties.

It is an easy and quick method of calculating an interest charge on a loan. Simple interest (S.I.) is determined by multiplying the principal (P) with rate of interest (R) and time period (T).

Example: Henry borrowed Rs. 5000 for 4 years at an interest rate of 5% from a bank. How much of interest is that?

We know,

Here P= Rs. 5000, R= 5%, T= 4 years

So,

Ans: Henry has to pay Rs. 1000 as interest.

Clearly, in S.I. the principal remains constant throughout. But the above method is not generally used in day to day financial system like banks, insurance companies, post offices. They use a different method of computing interest. In this method the lender and the borrower agree to fix up a certain time interval, say a year or half a year or a quarter of a year for the computation of the interest and the amount. At the end of the first interval, the interest is computed and is added to the original principal. The amount obtained is added to the second interval of time. The amount of this principal at the end of the second interval of time is taken as the principal of the third interval of time and so on. At the end of the certain specified period, the difference between the amount and money borrowed, that is, the original principal is computed and it is called the compound interest. Let us simplify it.

Compound Interest (CI)

If the borrower and lender agree to fix up a certain interval of time, so that the amount (Principal + Interest) at the end of the interval becomes the principal of the next interval, then the total interest over all the interests, calculated in this way is called the Compound Interest or C.I..

Evidently, C.I. at the end of a certain specified period is equal to the difference between the amount at the end of the period and the original principal.

C.I. = Amount – Principal

Conversion Period: The fixed interval of time at the end of which the interest is calculated and added to the principal at the beginning of the interval is called the conversion period. In other words, the period at the end of which the interest is compounded is called the conversion period. For instance, when the interest is calculated and added to the principal every six months, the conversion period is six months. Likewise, the conversion period is three months when the interest is calculated and added quarterly.

NOTE: If no conversion period is specified, the conversion period is taken to be one year.

Compound Interest Calculation from simple Interest where Interest is compounded annually.

Q1. Find the Compound interest on Rs. 10000 for two years at 5% per annum.

Solution: Principal for the first year = Rs. 10000

Interest for the first year =

[We are using the formula ]

amount at the end of first year = Rs 10000 + Rs. 500 = Rs. 10500

Interest for the second year =

Principal of the second year was Rs. 10500 and so amount at the end of the second year = Rs. 10500 + Rs. 525 = Rs. 11025

So, Compound interest= Rs. (11025 – 10000) = Rs. 1025

Note: The C.I. can also be found by adding the interest for each year.

Compound Interest Calculation from simple Interest where Interest is compounded half yearly.

If the rate of interest is R% per annum and the interest is compounded half-yearly, then the rate of interest will be R/2% per half year.

Q: Find the compound interest on Rs. 10000 for 1½ years at 20% per annum, interest being payable half-yearly.

Solution: We know, R= 20% per annum
or, 10% per half year.

T= 1½ years = 3 half years

Original Principal (P) = Rs. 10000

I for the first half-year =

P for the second half-year = Rs. 10000+1000= Rs. 11000

I for the second half-year =

Amount at the end of the second half-year = Rs. 11000 + Rs. 1100 = Rs. 12100

P for the third half year= Rs. 12100

I for the third half-year =

Amount at the end of third half-year = Rs. 12100 + Rs. 1210 = Rs. 13310

C.I. = Rs. 13310 – Rs. 10000 = Rs. 3310.

Computation of C.I. when Interest is compounded quarterly

If the rate of interest is R% per annum and the interest is compounded quarterly, then the rate of interest will be R/4% per quarter.

Q: Find the compound interest on Rs. 10000 for 1 year at 20% per annum, compounded quarterly.

Solution: We have, R= 20% per annum = 20/4 % = 5% per quarter

T= 1 year= 4 quarters

P for the first quarter= Rs. 10000

Interest for the first quarter =

Amount at the end of first quarter= Rs. 10000 + Rs. 500 = Rs. 10500

P for the second quarter = Rs. 10500

Interest for the second quarter =

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

P for the third quarter = Rs. 11025

Interest for the third quarter =

Amount at the end of third quarter = Rs. 11025 + Rs. 551.25 = Rs. 11576.25

P for the fourth quarter = Rs. 11576.25

Interest for the fourth quarter =

Amount at the end of fourth quarter = Rs. 11576.25 + Rs. 578.8125= Rs. 12155.0625

C.I. = Rs 12155.0625 – Rs. 10000 = Rs. 2155.0625 or Rs. 2155.06

Compound Interest formula

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

and, respectively.

Proof: We have,

P = Principal and rate of interest is R% per annum. Since the interest is given annually.

the interest after one year

Amount at the end of one year =

Now, this amount is taken as the principal for the second year.

the interest after the second year

Amount at the end of second year

Considering this amount as the principal of the third year, we have

The interest for the third year

Amount for the third year

Hence, if we go on like this further, we have

Amount at the end of n years

Type 1: When the interest is compounded annually

Q: Find the amount of Rs.8000 for 3 years, compounded annually at 10% per annum. Also find the C.I.

Here, P= Rs.8000, R= 10% per annum and n= 3 years.

Using the formula , we get

Amount for 3 years

Thus the amount after 3 years is Rs.10,648

And the C.I. = Rs. ( 10648 – 8000 ) = Rs. 2648.

Type 2: When the interest is compounded annually but rates are different for different years.

Let Principal = Rs. P, Time= 2 years, and let the rates of interest be p% per annum, during the first year and q% per annum during the second year.

Then the amount after 2 years

This formula can be similarly extended for any number of years.

Q: Find the amount of R.s. 50000 after 2 years, compounded annually; the rate of interest being 8% p.a. during the first year and 9% p.a. during the second year. Also, find the compound interest.

At what rate percent per annum compound interest would 8000 amount to 88200 in 2 years?

At what rate compounded annually will 80000 amount 88200 in 2 years?

At what rate per cent per annum will Rs 8000 amount to Rs 8820 in 2 years at compound interest?

In what time will Rs 8000 amount to Rs 8820 at 10% per annum interest compounded half yearly?