Answer to Question #160069 in Algebra for ..

Question

using visuals/examples if necessary to support your explanation, answer the following:

a) What is the major difference between simple interest and compound interest? Pretend that you are providing this explanation to your English teacher, parent, or sibling. 

b) Why does an investment that earns compound interest grow at a faster rate than an investment that earns simple interest? 

Answer 1

1. The major difference between simple interest and compound interest is that simple interest is based on principle amount whereas compound interest is based on the principle amount and the interest compounded for a cycle of period.

Simple Interest: It can be defined as the sum paid back for using the borrowed money, over a fixed period of time.

Formula: $S.I.=\frac{P*R*T}{100}$

where,

S. I. = Simple Interest

P = Principle amount

R = Rate of interest per annum

T = Time period (in years) given for that interest on principle amount.

Return Amount: The return is much lesser when compared to compound interest.

The Principle amount is constant.

Growth: The growth remains quite uniform in this method.

Interest Charge: The interest charged on is for the principle amount.

Compound Interest: It can be defined as when the sum principle amount exceeds the due date for payment along with the rate of interest, for a period of time.

Formula: $C.I.= P(1+\frac{R}{100})^t-P$

where,

C.I. = Compound Interest

P = Principle amount

R = Rate of interest per annum

T = time period in years

Return Amount: The return is much higher.

The Principle amount keeps on varying during the entire borrowing period.

Growth: The growth increases quite rapidly in this method.

Interest Charge: The interest charged on it is for the principle and accumulated interest.

2. The investment in compound interest grows at a faster rate than an investment earns in simple interest as simple interest computed on the principle amount whereas compound interest computed based on the principle amount as well as the interest accumulated for a certain period. This can be understand by an example given below.

Q. Mahendra Bahubali takes a loan from a bank of amount Rs.20000 at a interest rate of 5% per annum. find the simple interest and compound interest on the loan amount if loan time period is of 2 years.

Ans. Given that

P = Rs.20000

R = 5%

T = 2 years

Simple Interest:

$S.I=\frac{P*R*T}{100}$

$S.I.=\frac{20000*5*2}{100}$

$S.I.=Rs.2000$

Compound Interest:

$C.I.=P(1+\frac{R}{100})^t-P$

$C.I.=20000(1+\frac{5}{100})^2-20000$

$C.I.=20000(1.1025)-20000$

$C.I.=22050-20000$

$C.I.=Rs.2050$

we can see that $C.I.\gt S.I.$