DIFFERENCE BETWEEN COMPOUND AND SIMPLE INTEREST FOR 2 YEARS

The formula given below can be used to find the difference between compound interest and simple interest for two years.

The above formula is applicable only in the following conditions.

1. The principal in simple interest and compound interest must be same.

2. Rate of interest must be same in simple interest and compound interest.

3. In compound interest, interest has to be compounded annually.

Example 1 :

The difference between the compound interest and simple interest on a certain investment at 10% per year for 2 years is $631. Find the value of the investment.

Solution :

The difference between compound interest and simple interest for 2 years is 631.

Then we have,

P(R/100)² = 631

Substitute R = 10.

P(10/100)² = 631

P(1/10)² = 631

P(1/100) = 631

Multiply both sides by 100.

P = 631 x 100

P = 63100

So, the value of the investment is $63100.

Example 2 :

The compound interest and simple interest on a certain sum for 2 years is $ 1230 and $ 1200 respectively. The rate of interest is same for both compound interest and simple interest and it is compounded annually. What is the principal ?

Solution :

To find the principal, we need rate of interest. So, let us find the rate of interest first.

Step 1 :

Simple interest for two years is $1200. So interest per year in simple interest is $600.

So, C.I for 1st year is $600 and for 2nd year is $630.

(Since it is compounded annually, S.I and C.I for 1st year would be same)

Step 2 :

When we compare the C.I for 1st year and 2nd year, it is clear that the interest earned in 2nd year is 30 more than the first year.

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

It can be considered as simple interest for one year.

That is, principle = 600, interest = 30

I = PRT/100

30 = (600 x R x 1)/100

30 = 6R

Divide both sides by 6.

5 = R

So, R = 5%.

Step 3 :

The difference between compound interest and simple interest for two years is

= 1230 - 1200

= 30

Then we have,

P(R/100)² = 30

Substitute R = 5.

P(5/100)² = 30

P(1/20)² = 30

P(1/400) = 30

Multiply both sides by 400.

P = 30 x 400

P = 12000

So, the principal is $12000.

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