**Word Problems on Simple Interest :**

In this section, we are going to learn , how to solve word problems simple interest step by step.,

**Formulas related to simple interest :**

** A** = Accumulated value (final value )

** P** = Principal (initial value of an investment)

** r** = Annual interest rate

** I** = Amount of interest

** n** = number of years

**Problem 1 :**

Find the simple interest for 2 years on $2000 at 6% per year.

**Solution : **

Formula for simple interest is

I = Pnr / 100

Here, P = 2000, n = 2, r = 6

Let us plug these values in the above formula

I = (2000 ⋅ 2 ⋅ 6) / 100

I = 20 ⋅ 2 ⋅ 6

I = 240

Hence, the interest earned is $240.

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**Problem 2 :**

In simple interest, a sum of money doubles itself in 10 years. Find the number of years it will take to triple itself.

**Solution : **

Let P be the sum of money invested.

Given : Sum of money doubles itself in 10 years

Then, P will become 2P in 10 years.

Now we can calculate interest for ten years as given below

From the above calculation, P is the interest for the first 10 years.

In simple interest, interest earned will be same for every year.

So, interest earned in the next 10 years also will be P.

It has been explained below.

Hence, it will take 20 years for the principal to become triple itself.

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**Problem 3 :**

In simple interest, a sum of money amounts to $ 6200 in 2 years and $ 7400 in 3 years. Find the principal.

**Solution :**

At the end of 2 years, we get $6200

At the end of 3 years, we get $7400

From these two information, we can get the interest earned in the 3rd year as given below.

In simple interest, interest will be same for every year.

Based on this, we can calculate the principal as given below

Hence, the principal is $3800.

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**Problem 4 :**

A sum of $46875 was lent out at simple interest and at the end of 1 year 8 months, the total amount was $50000.Find the rate of interest per year.

**Solution : **

From the given information, we have

P = 46875 and A = 50000

Then,

Interest = Amount - Principal

I = 50000 - 46875

I = 3125

The value of "n" must always be in "years". But in the question, it is given in both years and months.

To convert months into years, we have to divide the given months by 12.

1 year 8 months = 1 8/12 years or 1 ⅔ years

So, the value of "n" is 1 ⅔ or 5/3.

Formula for simple interest is,

I = Pnr / 100

Here, P = 46875, n = 5/3

3125 = [46875 ⋅ 5/3 ⋅ r) / 100

312500 = 78125 ⋅ r

312500 / 78125 = r

4 = r

Hence, the rate of interest per year is 4%.

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**Problem 5 :**

Find the accumulated value of the deposit $2500 made in simple interest for 3.5 years at 5% rate of interest per year.

**Solution : **

First let us find the interest earned and then we can find the accumulated value.

I = Pnr / 100

Here, P = 2500, n = 3.5, r = 5

I = (2500 ⋅ 3.5 ⋅ 5) / 100

I = 25 ⋅ 3.5 ⋅ 5

I = 437.50

Accumulated value is,

A = P + I

A = 2500 + 437.50

A = 2937.50

Hence, the accumulated value is $2937.50

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**Problem 6 :**

How much interest will be earned on $3000 at 7% simple interest per year for 9 months ?

**Solution : **

Formula for simple interest is

I = Pnr / 100

Here, P = 3000, r = 7%

The value of "n" must always be in "years". But in the question, it is given in months.

To convert months into years, we have to divide the given months by 12.

9 months = 9/12 years or 3/4 years

So, the value of "n" is 3/4.

Then, we have

I = [3000 ⋅ 3/4 ⋅ 7] / 100

I = 30 ⋅ 0.75 ⋅ 7

I = 157.50

Hence, the interest earned is $157.50

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**Problem 7 :**

What sum of money will produce $28600 as interest in 3 years and 3 months at 2.5% per year simple interest ?

**Solution : **

Formula for simple interest is

I = Pnr / 100

Here, I = $28600, r = 2.5%

The value of "n" must always be in "years". But in the question, it is given in both years and months.

To convert months into years, we have to divide the given months by 12.

3 years 3 months = 3 3/12 years or 3¼ years

So, the value of "n" is 3¼ or 13/4.

Plug I = 28600, r = 2.5 and n = 13/4 in the formula of simple interest.

28600 = [P ⋅ 13/4 ⋅ 2.5] / 100

2860000 = P ⋅ 3.25 ⋅ 2.5

2860000 = P ⋅ 8.125

2860000 / 8.125 = P

352000 = P

Hence, the required principal is $352,000.

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**Problem 8 :**

Mr. Abraham invested an amount of $13900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be $ 3508, what was the amount invested in Scheme B ?

**Solution : **

Let "m" be the amount invested in scheme B.

Then the amount invested in scheme A = 13900 - m

Interest in scheme (A) + Interest in scheme (B) = 3508

(13900 - m) ⋅ 0.14 ⋅ 2 + m ⋅ 0.11 ⋅ 2 = 3508

(13900 - m) ⋅ 0.28 + 0.22m = 3508

3892 - 0.28m + 0.22m = 3508

3892 - 0.06m = 3508

3892 - 3508 = 0.06m

384 = 0.06m

m = 6400

Hence, the amount invested in scheme B is $6,400.

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**Problem 9 :**

Lily took a loan of $1200 with simple interest for as many years as the rate of interest. If she paid $432 as interest at the end of the loan period, what was the rate of interest?

**Solution : **

Let "m" be the rate of interest.

**Given :** The rate of interest and the number of years are same

Then, the number of years = m

Formuls for simple interest is

I = Pnr / 100

Here, I = $432, P = $1200, r = m , n = m

So, we have

432 = (1200 ⋅ m ⋅ m) / 100

432 = 12m²

36 = m²

6 = m

Hence, the rate of interest is 6%.

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**Problem 10 :**

A lent $5000 to B for 2 years and $3000 to C for 4 years on simple interest at the same rate of interest and received $2200 in all from both of them as interest. Find the rate of interest per year.

**Solution : **

Let "m" be the rate of interest

Interest from B + Interest from C = 2200

(5000 ⋅ m ⋅ 2) / 100 + (3000 ⋅ m ⋅ 4) / 100 = 2200

10000m + 12000m = 220000

22000m = 220000

m = 10

Hence, the rate of interest is 10%.

After having gone through the stuff given above, we hope that the students would have understood simple interest.

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