 ## Interest

Theory

The questions in this topic are fairly easy to solve if you know certain formulas and basics behind Simple Interest and Compound Interest. While solving the questions, write down the basic formulas to avoid the confusion and also memorize certain powers of fraction so that you can solve Compound Interests question easily.

For eg $${1.1}^2$$ = 1.21, $${1.1}^3$$ = 1.331 etc.

Theory

Simple Interest is the interest earned when the borrower usually pays a fee to the lender each year and that fee is usually a percentage of amount borrowed at the start.

Formula

Simple Interest is usually calculated using a simple

$$SI = \frac{P*R*T}{100}$$
SI = Simple Interest
P = Principal or amount borrowed or lent initially
R = Rate of Interest (per annum)
T = Time in years.

Theory

Compound Interest is the interest earned on the initial principal plus the interests earned over the previous periods of the loan. For eg. if Rs 100 is compounded annually at 10% p.a., then the principal for first year is Rs 100 and for the second year is Rs 100+ Interest earned during first year = Rs (100 + 10) = Rs 110.

Formula

Principal earned at the rate of interest compounded annually after a certain period of time can be calculated by using a

A = P $$[1+\frac{R}{100}]^n$$
A = Amount due
P = Initial principal
R = Rate of Interest (in % p.a.)
n = Time (years)

Formula

There is a special case of CI when the compounding is not done annually. In fact it is done compounded after 6 months, 4 months, 3 months etc.
The principal earned in this case is calculated using a simple

$$A = P[1+\frac{R}{x*100}]^{nx}$$
A = Amount due
P = Initial principal
R = Rate of Interest (in % p.a.)
n = Time (years)
x = Number of compounding
For eg. If interest is compounded semi-annually, then
x = 1/0.5 = 2

Solved Example

How much does Rs.1000 amount to in 2 years when it is deposited in a bank at 8% pa interest? The bank compounds interest semi-annually.

Explanation: Apply the formula

$$A = P[1+\frac{R}{x*100}]^{nx}$$
x = 1/0.5 = 2
$$A = 1000 [1+\frac{8}{2*100}]^{2*2}$$ = 1000 * $$(1+\frac {4}{100})^{4}$$ = 1170

Solved Example

The simple interest on a sum of money for 3 years at 8% p.a. is 240 rupees. What is the principal for this interest?

Explanation: Use the formula:

SI = (P*R*T)/100
240 = (P*3*8)/100
P = Rs 1000
Hence Principal =Rs 1000