"Simple interest problems" is much required to the students who study math in school level.

**Definition of Simple Interest :**

**Simple interest is the interest computed on the principal for the entire period of borrowing. It is calculated on the outstanding principal balance and not on interest previously earned.It means no interest paid on interest earned during the term of loan.**

**Key Concept :**

**Principal will always be constant****Interest for every year will be same**

**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 x 2 x 6) / 100

I = 20 x 2 x 6

I = 240

**Hence, the interest earned is $240**

Let us look at the next problem on "Simple interest problems"

**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.**

Let us look at the next problem on "Simple interest problems"

**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**

**Let us look at the next problem on "Simple interest problems"**

**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 $5000.Find the rate of interest per year.

**Solution : **

From the given information, we have

P = 46875 and A = 50000

Then, I = A - P

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 by 12.

Then, 1 year 8 months = 1 8/12 years or 1 2/3 years

So, n = 5/3

Formula for simple interest is,

**I = Pnr / 100 **

Here, P = 46875, n = 5/3, r = ?

3125 = [46875 x (5/3) x r) / 100

312500 = 78125 x r

312500 / 78125 = r

4 = r

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

Let us look at the next problem on "Simple interest problems"

**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 x 3.5 x 5) / 100

I = 25 x 3.5 x 5

I = 437.50

Accumulated value, ** A = P + I **

A = 2500 + 437.50

A = 2937.50

**Hence, the accumulated value is $2937.50**

Let us look at the next problem on "Simple interest problems"

**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 by 12.

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

So, n = 3/4

Then, I = [3000 x (3/4) x 7] / 100

I = 30 x 0.75 x 7

I = 157.50

**Hence, the interest earned is $157.50**

Let us look at the next problem on "Simple interest problems"

**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%, P = ?

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 by 12.

Then, 3 years 3 months = 3 3/12 years or 3 1/4 years

So, n = 13/4

Then, 28600 = [P x (13/4) x 2.5] / 100

2860000 = P x 3.25 x 2.5

2860000 = P x 8.125

2860000 / 8.125 = P

352000 = P

**Hence, the required principal is $352000**

Let us look at the next problem on "Simple interest problems"

**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) x 0.14 x 2 + m x 0.11 x 2 = 3508

(13900 - m) x 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 $6400**

Let us look at the next problem on "Simple interest problems"

**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, 432 = (1200 x m x m)/100

432 = 12m²

36 = m²

6 = m

**Hence, the rate of interest is 6%**

Let us look at the next problem on "Simple interest problems"

**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 x m x 2) / 100 + (3000 x m x 4) / 100 = 2200

10000m + 12000m = 220000

22000m = 220000

m = 10

**Hence, the rate of interest is 10%**

**More Quantitative Aptitude Topics**

**10. Problems on Boats and Streams**

**11. Problems on Ratio and Proportion**

**16. Compound Interest Problems**

**17. Permutation and Combination Problems**

**22. Word Problems on Simple Equations**

**23. Word Problems on Simultaneous Equations**

**24. Problems on Quadratic Equations**

**25. Word Problems on Quadratic equations**

**26. Pipes and Cisterns Shortcuts**

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