Monday , September 24 2018
Calculators

How to calculate Interests

What is interest?? When we look at dictionary the literal meaning of interest is “something that concerns, involves, draws the attention of, or arouses the curiosity of a person”. Money is something which draws the attention of all.  We do not lend money free of cost to anyone especially when it is banking transactions. When we deposit money in saving bank account we get interests on it. When we deposit same money in fixed deposit account we get more interest on it. Same money deposited in PPF account will give even more interests. How do these accounts have different interest for same money deposited? how they calculate interests ?? First Reason is that these accounts have different rate of interest.  Second reason is that they have the different method of calculating interests. There are two method of calculating interests. These methods are listed here and discussed in detail below.

  • Simple Interests
  • Compound Interests

Also Read, How Banks calculate Saving account interests

How to calculate Simple Interests

Simple interest is applied to the amount borrowed or invested for certain duration of time. In this case the interest is calculated on the principal amount only. The interests are not calculated for the past interests paid or any other financial considerations. It is very simple to calculate. Simply multiply the principal amount with the rate of interests and duration of investments.

The formula for simple interests is as follows

SI = \frac{P . r . t }{ 100 }.

P-Principal amount or money invested / borrowed.
r-rate of interest. It is expressed in percentage of interest per annum.
t- Time of investment / borrowed

Example. A bank lends you Rs. 50,000 at a simple annual interest rate of 3%. How much interest do you owe 10 years later?

P = Rs. 50,000

r = 0.03/year (To convert a percentage to a decimal, divide by 100.)

t = 10 years

SI = P.r.t = (50,000)(0.03/year)(10 years) = Rs.15,000

Total amount owed after 10 years  = Rs.50,000 + Rs.15,000 = Rs.65,000.

How to calculate Compound Interests

Compound interest is applied when the borrower is ready to pay the interests of the interests money. In this method the interests is added to the principal amount when the interests is paid, therefore the next time interest is calculated on principal and earlier interests accumulated. The act of giving interest on interest is called compounding. The period of compounding is declared by the borrower or the bank. It means when the interest will be calculated and added to the principal amount will be declared initially. Financial institutions vary in terms of their compounding rates – daily, monthly, quarterly, half-yearly, yearly, etc.

The formula for calculating compound interest is as follows:

In this method we usually calculate the total future value of investment. Interest is obtained by subtracting the principal amount from the total future value.

V = P.(1+\frac{r}{n})^{(n.t)}

V = the future value of the investment
P = the principal investment amount
r = the annual interest rate
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

Total Interest , CI = V - P

Example. Consider same example, A bank lends you Rs. 50,000 at an annual interest rate of 3% compounded quarterly. How much interest do you owe 10 years later?

P = Rs. 50,000

r = 0.03/year (To convert a percentage to a decimal, divide by 100.)

t = 10 years

n= 4

V = P.(1+\frac{r}{n})^(n.t) = (50,000)(1+0.03/4)(4*10 years) = Rs. 67417.43

Therefore CI = V – P = Rs. 67417.43 – 50000 = Rs. 17417.43

This shows that compound interests is always more than simple interest for the same time and rate of interest. The money invested with compounded interest grows faster. This is a double edge sword also, while investment it is beneficial where in the case of borrowing it is dangerous. For example if credit card bills are not paid within due date the bank will charge interests on bill amount, and if it is not paid next month also it will charge interests on interests and the dues become huge.

How long it takes to double your money:

There are schemes which claim to double your investment in certain period of time. Now how do they calculate the time lets see.

V = 2P [ future investment become double of principal amount]

Therefore,

2P = P.(1+r)^{(t)} [suppose n=1]

or, 2 = (1+r)^{(t)}

t= \frac{log(2)}{log(1+r)}

t= \frac{log(2)}{log(1.06)} =11.9 or 12 years [ rate of interest =6%]

The Rule of 72

This is a simple method to calculate the time to double the invested money. It is simple and reasonably correct if the interest rate is below 20%. The rule of 72 say that divide number 72 by the rate of interest to find the time of investment to double the money. Taking example of above calculation, if the rate of interest is 6% than 72/6=12 i.e twelve years to double the money.

t = \frac{72}{ r}

t= time to double the invested money

r=rate of interest

Authored by howtocalculate

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