INTRODUCTION
Interest is the money paid to the lender by the borrower for using his money for a specified period of time. Various terms and the general representation are as follows:
Compound Interest Definition:
The amount at the end of first year (or period) will become the principal for the second year; the amount at the end of second year becomes the principal for the third year and so on.
Under Compound Interest, the interest is added to the principal at the end of each period to arrive at the new principal for the next period.
Formulae Related to 'compound Interest':
Let principal = Rs. P, Time = t years, Rate = r% per annum and A = Amount, (i.e. Principal Amount + Interest)
1. General Formula: $Amount = P[ 1+\frac{\frac{r}{n}}{100}]$nt
Case 1: When interest is compounded annually:
$Amount = P[ 1+\frac{r}{100}]$t
Case 2: When interest is compounded half-yearly:
$Amount = P[ 1+\frac{\frac{r}{2}}{100}]$2t
Case 3: When interest is compounded quarterly:
$Amount = P[ 1+\frac{\frac{r}{4}}{100}]$4t
2. When rate of interest is $r_1$ %, $r_2$ %, $r_3$ % for 1st year, 2nd year and 3rd year respectively.
$Amount = P[1+\frac{r_1}{100} ]*[1+\frac{r_2}{100} ] * [1+\frac{r_3}{100} ] $
3. Compound interest = Amount - Principle
$ = P(1+\frac{r}{100} )^t - P$
Terms Related to 'compound Interest'
Interest
Interest is the money paid by borrower for using the lender's money, I denotes Interest.
Principal
The original sum borrowed is termed as principal, P denotes Principal.
Time
Time for which money is borrowed, t denoted time period. (t is expressed in number of periods, which is normally one year)
Rate Of Interest
Rate at which the interest is calculated on the original sum is called Rate Of Interest. It is denoted by r and is expressed as a percentage or decimal fraction.
Amount
Sum of principal and interest, A denotes amount.
Examples Problems on 'compound Interest'
1. Find the amount on $ 5000 for 3 years at 10% per annum compound interest.
Sol: $A = P[1+\frac{r}{100*n}]$nt
Here, P = $ 5000, r = 10% P.a
t = 3years, n = number of conversions per year = 1
$A = 5000[1+\frac{10}{100}]^3$
= 5000 x 1.1 x 1.1 x 1.1 = 6655
Therefore, the amount is $6655.
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2. If the interest is compounded annually, find the compound interest on $3000 for 4 years at 10% p.a
Sol: C.I. = $P[(1+\frac{R}{100})^t - 1]$
= $3000[(1+\frac{10}{100})^4 - 1]$
= $3000[(\frac{11}{10})^4 - 1]$
= $3000[\frac{14641-10000}{10000}]$
= $3000[\frac{4641}{10000}]$
= $1392.3
Therefore, the Compound Interest is $1392.3
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3. Find the amount, if you deposit $5000 in a bank and receive 5% per year compound interest for 5 years, compounded monthly. Find the amount after 5 years.
Sol: $A = P * [1+(\frac{r}{n})]$nt
= $A = 5000 * [1+(\frac{0.05}{12})]$12*5
= $5000 * [1.0041]$60
= 6391.28
Interest gained = Amount - principal
= 6391.28 - 5000
= 1391.28
The total interest gained is $1391.28
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Related Tags
Explain Compound Interest , What is Compound Interest , Introduction to Compound Interest