**Simple Interest Problems with Solutions :**

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

Before look at the problems, let us see the definition and key concept of simple interest.

**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**

Formula to find Simple Interest :

**I = Prt**

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

** r** = Annual interest rate

** ****t** = number of years

**Problem 1 :**

A person deposits $5,000 in a bank account which pays 6% simple interest per year. Find the value of his deposit after 4 years.

**Solution : **

Formula for simple interest is

I = Prt

Here, P = 5000, t = 4, r = 6%

Let us plug these values in the above formula

I = 5000 ⋅ 6/100 ⋅ 4

I = 1200

The formula to find the accumulated value is

= Principal + Interest

= 5000 + 1200

= 6200

Hence, the value of his deposit after 4 years is $6,200.

Let us look at the next problem on "Simple interest examples".

**Problem 2 :**

Glen received $2,250 loan from bank. After six months, he paid back $2,295 and closed the loan. Find the rate of interest.

**Solution : **

Interest = Amount - Principal

I = 2295 - 2250

I = 45

Formula for simple interest is

I = Prt

**Given :** Time period is 6 months.

In simple interest formula, we use time period in years. But, the time period given in the question is in months.

So, let us change the given time period in years.

6 months = 6 / 12 year

6 months = 1 / 2 year

So, the time period is 1/2 year.

Formula for simple interest is

I = Prt

Here, I = 45, P = 2250, t = 1/2

Let us plug these values in the above formula

45 = 2250 ⋅ r ⋅ 1/2

45 = 1125 ⋅ r

Divide both sides by 1125.

45 / 1125 = r

0.04 = r

To convert the decimal 0.04 into percentage, multiply it by 100.

0.04 ⋅ 100 % = r

4 % = r

Hence, the rate of interest is 4%.

Let us look at the next problem on "Simple interest examples".

**Problem 3 :**

A man invests $16,500 in two kinds treasury notes, which yield 7.5% and 6% annually. After two years year, he earns $2,442 in interest. How much does he invest at the 6 % rate ?

**Solution : **

Let "x" be the amount invested at 6% rate.

Then, the amount invested in 7.5% account is

= 16500 - x

**Given :** After two years, total interest earned in both the accounts is $2,442.

So, we have

Interest at 6% rate + Interest at 7.5% rate = 2442

x ⋅ 6/100 ⋅ 2 + (16500 - x) ⋅ 7.5/100 ⋅ 2 = 2442

x ⋅ 0.06 ⋅ 2 + (16500 - x) ⋅ 0.075 ⋅ 2 = 2442

0.12x + (16500 - x) ⋅ 0.15 = 2442

0.12x + 2475 - 0.15x = 2442

2475 - 0.03x = 2442

2475 - 2442 = 0.03x

33 = 0.03x

Divide both sides by 0.03

33 / 0.03 = x

3300 / 3 = x

1100 = x

Hence, the amount invested at 6% rate is $1,100.

**Problem 4 :**

A person invested $25,200 in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years year, he earns $2,442 in interest. How much did he invest at the 5% rate ?

**Solution : **

Let "x" be the amount invested at 5% rate.

Then, the amount invested in 10% account is

= 110% of x

= 1.10 ⋅ x

= 1.1x

**Given :** After three years, total interest earned in both the accounts is $5,760.

So, we have

Interest at 5% rate + Interest at 10% rate = 5760

x ⋅ 5/100 ⋅ 3 + 1.1x ⋅ 10/100 ⋅ 3 = 5760

x ⋅ 0.05 ⋅ 3 + 1.1x ⋅ 0.1 ⋅ 3 = 5760

0.15x + 0.33x = 5760

0.48x = 5760

Divide both sides by 0.48

x = 5760 / 0.48

x = 576000 / 48

x = 12000

Hence, the amount invested at 5% rate is $12,000.

**Problem 5 :**

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 examples".

**Problem 6 :**

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.

After having gone through the stuff given above, we hope that the students would have understood the stuff "Simple interest problems with solutions".

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