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:
Simple Interest Definition:
If the interest on a certain sum borrowed for a certain period is reckoned uniformly, then it is called Simple Interest.
Simple Interest is denoted as S.I.
If a person A borrows some money from another person B for a certain period, then after that specified period, the borrower has to return the money borrowed as well as some additional money. This additional money that borrower has to pay is called interest. The actually borrowed money, A is called principal (SUM). The principal and the interest together is called amount. The interest that the borrower has to pay for every 100 dollars borrowed for every year is known as rate percent per annum.
It is denoted as R% per annum = $\frac{R}{100}$
The time for which the borrowed money has been used in called the time. It is denoted as T years.
The interest is directly proportional to the principal, the rate and the time for which the borrowed sum is used.
Formula Related to 'simple Interest':
Simple Interest (S.I) = $\frac{P * T * R}{100}$
Therefore, if the value of P, R or T changes, then the value of simple interest will also change.
Total Amount (A) = Principal + Simple Interest.
Terms Related to 'simple 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.
Example Problems on 'simple Interest':
1. What principal will yield $90 as simple interest as 9% per annum in 10 years?
Sol: Simple Interest = $\frac{P * T * R}{100}$
Principal = $\frac{S.I * 100}{R * T}$
= $\frac{90 * 100}{9 * 10}$
= $100
______________________________________________________
2. What is the interest Alex has to pay on a sum of $1000 at the end of 3 years at 6% per annum simple interest?
Sol: Simple Interest = $\frac{P * T * R}{100}$
= $\frac{1000 * 3 * 6}{100}$
= $180
_____________________________________________________
3. What principal will amount $570 at 4% per annum in 3 years?
Sol: Amount = Principal + Simple Interest
A = P + $\frac{P * T * R}{100}$
A = $\frac{P}{100}(100 + TR)$
P = $\frac{100A}{100+TR}$
= $\frac{100 * 570}{100+4 * 3}$
= $508.9
______________________________________________________
4. A Sum of $5000 amounts to $7500 in 5 years under simple interest. What will $6000 amount to at the end of 4 years at the same rate of simple interest?
Sol: Amount = P + $\frac{P * T * R}{100}$
7500 = 5000 + $\frac{5000 * 5 * R}{100}$
2500 = 250R
R = 10% p.a.
In 4 years, Rs. 6000 amounts to
= 6000 (1 + $\frac{4 * 10}{100}$)
= 6000 (1 + $\frac{2}{5}$)
= 6000 * $\frac{7}{5}$
= $8400
______________________________________________________
5. It takes 10 years for a sum to double at a certain rate of simple interest. Find the time it takes to triple itself at the same rate of simple interest.
Sol: Let the rate of interest be R% p.a.
Let the sum be Rs. P.
Then if the amount = Rs.2P,
2P = P (1 + $\frac{10 * R}{100}$)
200 = 100 + 10R
10R = 100
? R = 10
Let the required time be t years
3P = P (1 + $\frac{10 * t}{100}$)
t = 20 years.
______________________________________________________
6. A sum was lent at simple interest for 2 years. If the sum was $10000 more, it would fetch $2000 more as simple interest when lent for the same time at the same interest rate. Find the rate of interest.
Sol: Let the rate of interest be R% p.a.
Additional interest = (10000) * $(\frac{R}{100})$ * (2) = 2000
R = 10%
______________________________________________________
7. A sum of $6000 was divided into two parts. One part was invested at 10% p.a. simple interest and the other part was invested at 20% p.a. simple interest. Both were invested for a year. The total simple interest earned was $840. Find the sum invested at 10% p.a.
Sol: Let the sum invested at 10% p.a. be $x.
Sum invested at 20% p.a. = $(6000 - x)
(x) $(\frac{10}{100})$ + (6000 - x) $(\frac{20}{100})$ = 840
x = $3600
______________________________________________________
8. A sum took 5 years to double at a certain rate of simple interest. Find the time it would take to triple at the same rate of simple interest (in years).
Sol: Let the rate of simple interest be R% p.a.
Let the sum be Rs. P
Let the required time be t years.
2P - P = P $(\frac{R}{100})$ (5)
R = 20
3P - P = P $(\frac{R}{100})$ t
2P = $\frac{20Pt}{100}$
t = 10 years.
Related Tags
Help with simple intrest online, Simple Interest and word problems, Online help with Simple intrest.