## Compound Interest Word Problems

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## How To Solve Compound And Simple Interest Problems Quickly

## How To solve Compound Interest And Simple Interest Problems Quickly

SI = {\frac{P × R × T}{100}} and CI = {P (1+ \frac{R}{100\times n})^{nT} – P}

## Definition of Simple and Compound Interest

- Compound Interest is the interest charged on the original principal and on the accumulated past interest of a deposit is known as Compound interest.
- Basically , The formula for Amount in Compoun interest , Amount = \mathbf{P × (1 + \frac{r}{100\times n})^{nT}}
- Simple Interest is the interest When some money is borrowed by someone, then borrower is required to pay an additional amount of money other than the original sum. This additional amount of money is called interest.
- Basically , the formula for Simple Interest, SI = \mathbf{\frac{P * R * T}{100}}
- Tips and Tricks to solve Simple and Compound Interest quickly
- Formulas to solve simple interest & compound interest
- Questions of Simple and Compound Interest.

## Type 2: Solve Simple Interest and Compound Interest Quickly. Find the amount/time/rate of interest when CI or SI or their difference is given

Solution The difference between compound interest and simple interest for three years is 31.

Solution Sum = \frac{500 × 100 }{2 × 5}

Amount = 5000 (1+ \frac{5}{100})^{2}

Solution CI – SI = \frac{P × (R)^2}{(100)^2}

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## COMPOUND INTEREST PROBLEMS

The formula to find accumulated value in compound interest is

A ----> Accumulated value (final value)

P ----> Principal (initial value of an investment)

r ----> Annual interest rate (in decimal)

n ----> Number of times interest compounded per year

Then, the accumulated value is

Let P be the amount invested initially. From the given information,

Simple interest for two years is 1200 and interest for one year is 600.

So, compound interest for 1st year is 600 and for 2nd year is 630.

(Since it is compounded annually, simple interest and compound interest for 1st year would be same)

Because, interest 600 earned in 1st year earned this 30 in 2nd year.

It can be considered as simple interest for one year.

That is, principal = 600, interest = 30.

In the given problem, simple interest earned in two years is 1200.

So, the principal is $ 12,000.

To find the accumulated value for the first year,

Substitute P = 15000, r = 0.12, n = 1 and t = 1 in the above formula.

Amount paid at the end of 1st year is 7000.

This 9800 is going to be the principal for the 2 nd year.

So, to completely discharge the loan, at the end of 2nd year, Mr. David has to pay $ 10,976.

Let the principal in simple interest be $100.

Since there is 60% increase, simple interest = 60

We already know the formula for S.I.

To know compound interest for 3 years,

Substitute P = 12000, r = 0.1, n = 1 and t = 3 in the formula of C.I.

So, the compound interest after 3 years at the same rate of interest is $3972.

Kindly mail your feedback to [email protected]

We always appreciate your feedback.

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## Question Video: Solving Word Problems Involving Compound Interest Mathematics • 9th Grade

## Video Transcript

## How to solve Compound Interest Problems

How to find compound interest / how to calculate compound interest using formula, sharing buttons:.

00:00 hello everyone today in this video we

00:02 are going to learn how to find compound

00:05 using formula so the formulas we are

00:09 i will be solving two examples in this

00:13 and the formulas we are going to use are

00:16 is when the interest is compounded

00:20 yearly the second one is when the

00:23 interest is compounded half yearly

00:25 we are going to solve one example of

00:27 each so the first formula is

00:30 amount is equal to principal time

00:33 1 plus r over 100 whole raised to power

00:37 n where a is the amount p

00:40 is the principle r is the rate of

00:43 and n is the number of years so when we

00:48 we are going to use the formula for

00:50 compound interest which is

00:52 amount minus principle so we will get

00:58 the next one is when the interest is

01:03 so when the interest is compounded half

01:05 yearly half yearly means

01:06 so there will be two half years in one

01:10 the n will become 2 n and the rate of

01:14 half which is r over 2 so our formula

01:19 a is equal to p times 1 plus

01:23 r over 200 whole raised to power

01:27 to n with the use of the formula

01:30 amount minus principle we can get the

01:34 interest so let's get started with our

01:37 example where the interest is compounded

01:41 yearly let's solve our first example

01:44 where our principal amount is 6000

01:48 and it is been kept or it is being

01:50 compounded for two years

01:52 with the rate of interest of 9 annually

01:56 so we need to find the compound interest

01:59 so we'll use the formula for amount

02:02 which is a is equal to p

02:12 and after finding the amount we can find

02:16 using the formula compound interest is

02:19 equal to amount minus principle

02:22 so our principle is 6000 rupees

02:26 so we'll put 6000 p is 6000

02:29 now we'll put the values in the formula

02:36 over 100 raised to power

02:46 this will give us 100 plus 9

02:50 over 100 raised to power 2

02:56 then this is 6 000 so this is 109

03:05 and after solving this gets multiplied

03:16 hundred so our amount will come out to

03:22 this gets cancelled three zeros gets

03:27 so we are left we are left with six

03:36 over 10. so amount comes out to be

03:41 after solving this comes out to be

03:52 so this is our amount now we need to

03:55 compound interest so compound interest

04:00 is equal to amount minus principle

04:12 minus the principal amount is 6000

04:16 so our compound interest comes out to be

04:26 so this is compound interest when sixth

04:30 house principal amount of six

04:31 thousand is compounded annually for two

04:34 years with a rate of interest of nine so

04:36 these are the steps you need to follow

04:39 to find the compound interest using the

04:43 when the amount is compounded annually

04:46 let's take one more example where the

04:50 semi-annually or half yearly so this is

04:54 where the we have to find the compound

04:56 interest when the principal of 8000

04:59 rupees at a rate of 10 percent per annum

05:02 and for one year is compounded half

05:06 so let's use our formula which we have

05:10 amount will become a is equal to

05:17 over 200 200 because it is

05:21 compounded half yearly raise to power

05:24 2 n so this is our formula for

05:28 amount is compounded half yearly so

05:31 we'll substitute or put the values here

05:38 one plus r is ten percent

05:43 over two hundred raised to power two

05:46 one so this will become eight

05:54 1 over 20 raised to power 2

05:59 so this is going to be 8 000

06:12 twenty one over twenty square

06:33 this is our amount so amount is equal to

06:37 the zeros gets cancelled

06:47 times 21 times 21 amount will become

06:55 so this is our amount and we need to

07:00 interest which will be amount minus the

07:08 minus the principal is 8000

07:13 so compound interest will be 820

07:19 rupees so this is our final answer

07:23 when the interest is compounded half

07:27 so these are the steps you need to

07:28 follow to find the compound interest

07:31 when the interest is compounded half

07:34 i hope this is helpful to you thanks for

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## Compound interest word problems

We will use the compound interest formula to solve these compound interest word problems.

B = 3000( 1 + 1%) 8 = 3000(1 + 0.01) 8 = 3000(1.01) 8 B = 3000(1.082856) B = 3248.57

After four years, there will be 3248.57 dollars in the bank account.

B = 2150( 1 + 1.5%) 24 = 2150(1 + 0.015) 24 = 2150(1.015) 24 B = 2150(1.4295) B = 3073.425

After 6 years, there will be 3073.425 dollars in the bank account.

B = 495( 1 + 3%) 3 = 495(1 + 0.03) 3 = 495(1.03) 3 B = 495(1.092727) B = 540.89

After 3 years, there will be 540.89 dollars in the bank account.

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Compound Interest Word Problems:Videos:YouTube - Video. Text Lessons:CK-12 - Text Lesson. Purple Math - Text Lesson. Worksheets:Khan Academy - Practice

The Basic Difference Between Simple Interest (SI) and Compound Interest(CI) is that the Simple Interest is the interest calculated on the Principal or sum of amount while Compound Interest is calculated on the

Because the investment is in compound interest, the principal in the 4th year will be 2P.And 2P becomes 4P (it doubles itself) in the next 3 years. The compound interest and simple interest on a certain sum for 2 years is $ 1230 and $ 1200 respectively

Bank A offers depositors 4% annual interest compounded once per year. And in bank A, that compound interest is applied once per year, so that means that we can use this simpler compound interest formula: 𝑉

3 Answers. use the formula (and its variations) relating P_0 the beginning principal, “r” the percent interest rate, and P_c the current principal after time T in terms of compounding period (typically in months or years)

We will use the compound interest formula to solve these compound interest word problems. Example #1 A deposit of $3000 earns 2% interest compounded semiannually