Lesson Interest rate calculation for compound interest

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This Lesson (Interest rate calculation for compound interest) was created by by Shruti_Mishra(0) About Me : View Source, Show
About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.
Compound Interest

Compound interest is the money charged by the lender on the principal and the interests which is accumulated till that time period. In the case of Compound interest there is a provision of the interest on interest.


The formula for the calculation of Compound Interest is

Amount+=+Principal+%2A+%281+%2B+Rate%2F100%29+%5EYears
Interest+=+Amount+-++Principal

Example:  We deposit money with the bank. The bank not only pay us back our initial deposit but also provide us with some kind of cash benefits (in the form of interest) for keeping the money with them. Suppose that you deposit the sum of $100 with the bank for the period of 5 yrs and the bank agrees to pay you the interest at the rate of 10%.

At the end of the first year you will get the interest of Rs 10 deposited in your account. In the second apart from getting the fixed interest of Rs 10, you will also get the interest on the accumulated interest till that time period i.e.  10% * $10 = 0.1 * $10 = $1

So the final amount in the second year will be 100 + 10 + 11 = 121

In case of Compound Interest the interest itself earns interest. The working for above example:


Year

Principal

Amount

Interest

1

100

100 * ( 1 + 0.1) = 110

110 – 100 = 10

2

110

100 * ( 1 + 0.1) (1 + 0.1) = 121

Or

110 * ( 1 + 0.1)^2 = 121

121 – 110 = 11

3

121

100 * ( 1 + 0.1) (1 + 0.1)(1 + 0.1) = 133.1

Or

121 * (1 + 0.1)^3 = 133.1

133.1 – 121 = 12.1

 

While Calculating Compound interest we observed that every year the Principal is equal to the Amount calculated last year.

Formulae when the compounding is not done annually


Compounded Semi- annually (Rate becomes half and time doubles)

Amount+=+Principal+%2A%28%281+%2B+%28Rate%2F200%29%29+%5E+%282%2ATime%29%29
Interest+=+Amount+-+Principal

Compounded quarterly (Rate becomes one fourth and Time becomes four times)

Amount+=+Principal+%2A%28%281+%2B+%28Rate%2F400%29%29+%5E+%284%2ATime%29%29
Interest+=+Amount+-+Principal

Compounded Monthly (Rate becomes one twelfth and Time becomes twelve times)

Amount+=+Principal+%2A%28%281+%2B+%28Rate%2F200%29%29+%5E+%282%2ATime%29%29
Interest+=+Amount+-+Principal

Also see:
Lessons:
Basics of Interest Rates and its uses
Simple Interest
Solvers:

Calculate Compound Interest, given Principal, Time and Interest Rate

Calculate Interest Rate, given Principal, Compund Interest and Time
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