You lend some amount of money to a person for a certain period of time upon the condition that the borrower pays back the amount with certain interest on the amount lent. So, in essence you are collecting a fee from the borrower for the amount you lent. In this topic we will deal with problems of this kind which is primarily concerned with the simple interest on the amount that is originally lent, borrowed or invested.
The first section in this topic is an introduction to Simple Interest with an explanation of the terminologies involved, the formula used to compute Simple Interest. The exercises contain solved question and answers on Simple Interest. When solving exercises, we recommend you to try solving the problems on your own, that way you will understand better and you can define your own approach to solving problems on Simple Interest.
Introduction to Simple Interest
Simple Interest is the extra amount that is paid (or charged) on the amount borrowed (or invested). It is denoted by SI.
SI is generally calculated every year (or every time period) on the original Principal.
Principal: The amount borrowed (or invested) is called the Principal generally denoted by P.
Amount: Denoted by A is the final value of principal with interest.
Rate of interest: Is the annual simple interest rate. Denoted by r.
Interest: Denoted by I. Is the extra amount by which the principal increases.
Time period: Is the time interval for which the money is borrowed (or invested). Denoted by n.
Computing Simple Interest:
SI = $\frac{Pnr}{100}$
Final Amount = P + SI
Important Points:
- The Simple Interest earned every year is constant.
- The principal is same at the beginning of every year.
Problems
Simple Interest - Exercise - Blog
15 questions
- A certain sum of money amounts to Rs. 5600 in first 2 years and Rs. 5900 in first 3 years. Find the sum. Assume SI.
- Rs. 4500
- Rs. 4750
- Rs. 5000
- Rs. 5250
Show the answer
Answer: Rs. 5000
In SI, the interest is same every year. Hence, lets first find the interest per year using the information in the problem.
Given, amount after 2 years is Rs. 5600 and amount after 3 years is Rs. 5900
Interest in third year = Amount at the end of third year - Amount at the beginning of third year
= 5900 - 5600 = 300
Hence, the interest per year is Rs. 300. Now we can find the sum using the amount at the end of 2 years or 3 years and the interest per year
Sum = Amount after 2 years - 2 x (Interest per year)
= 5600 - 2 x 300
= Rs. 5000
- A man deposits an amount of Rs. 3000 for 3 years and Rs. 4000 for 4 years at a certain rate of SI and gets Rs. 1000 as interest from both the deposits. Find the rate of the interest.
- 4% p.a
- 2% pa
- 5% pa
- 7% pa
Show the answer
Answer: 4% p.a
Let the rate of interest be r.
SI =$\frac{\text{P1 x r x t1}}{100} +\frac{\text{P2 x r x t2}}{100}$
1000 =$\frac{\text{3000 x r x 3}}{100} +\frac{\text{4000 x r x 4}}{100}$
90r + 160r = 1000
250r = 1000
r = 4
Hence the rate of interest is 4% p.a
- Find the principal amount that gives an interest of Rs. 675 at 9% p.a in 3 years. Assume SI.
- Rs. 1000
- Rs. 2000
- Rs. 2500
- Rs. 1500
Show the answer
Answer: Rs. 2500
SI = 635, r = 9, t = 3, P=?
SI =$\frac{\text{P x r x t}}{100}$
675 =$\frac{\text{P x 9 x 3}}{100}$
P = Rs. 2500
Hence, the principal amount is Rs. 2500
- What is the time taken to get an interest of Rs. 162 on a sum of Rs. 900 at 6% rate of simple interest pa?
- 5 years
- 3 years
- 7 years
- 4 years
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Answer: 3 years
SI = 162, P = 900, r = 6, t = ?
SI = $\frac{\text{P x r x t}}{100}$
162 = $\frac{\text{900 x 6 x t}}{100}$
t = $\frac{162}{54}$
t = 3 years.
Hence, it takes 3 years to get an interest of Rs. 162 on the given sum of Rs. 900 at 6% p.a
- Find the SI for a period of 2 years and 4 months. Given Principal is Rs. 1500, Rate of interest is 10 % per annum.
- 350
- 500
- 200
- 450
Show the answer
Answer: 350
SI = ?, P = 1500, r = 10, t =$\frac{\text{2x12 + 4}}{12}$ = $\frac{28}{12}$ = $\frac{7}{3}$
SI =$\frac{\text{P x r x t}}{100}$
=$\frac{\text{1500 x 10 x 7}}{\text{3 x 100}}$
= 350
- A person deposits R. 10000 in a bank at 6% p.a rate of simple interest. 8 months after he deposited the amount he withdraws Rs. 5000 from the bank. 1 year after he deposited the amount he withdrew the remaining Rs. 5000 from the bank. How much amount did the person receive in interest.
- Rs. 1000
- Rs. 1500
- Rs. 500
- Rs. 750
Show the answer
Answer: Rs. 500
Amount deposited in the bank for 1 year is Rs. 5000 and for 8 months is Rs. 5000
Interest received = Interest on the amount deposited for 1 year + Interest on the amount deposited for 8 months
=$\frac{\text{5000 x 6 x 1}}{100} +\frac{\text{5000 x 6 x 8}}{(12\text{ x }100)}$
= 300 + 200
= Rs. 500
The interest amount received by the person = Rs. 500
- If you invest Rs. 1000 at the 10%p.a rate of Simple Interest. How much interest will you earn in 6 and half years?
- Rs. 500
- Rs. 650
- Rs. 700
- Rs. 750
Show the answer
Answer: Rs. 650
SI = ?, P = Rs. 1000, r = 10% p.a
t = 6 $\frac{1}{2}$ years = $\frac{13}{2}$ years
SI =$\frac{\text{1000 x 10 x 13}}{\text{2 x 100}}$
= Rs. 650
- If you want to get Rs. 500 in interest at the end of 10 months at 12% rate of interest. How much should you invest now?
- Rs. 2500
- Rs. 3000
- Rs. 5000
- Rs. 10000
Show the answer
Answer: Rs. 5000
SI = Rs. 500, r = 12, t =$\frac{10}{12}$, P = ?
SI =$\frac{\text{P x r x t}}{100}$
500 = $\frac{\text{P x 12 x 10}}{\text{12 x 100}}$
P = Rs. 5000
- At what rate of interest should an amount of Rs. 600 be invested to earn at the end of 5 years the same interest as earned by investing Rs. 500 at 6% pa for 3 years at SI.
- 3% p.a
- 5% p.a
- 6% p.a
- 4% p.a
Show the answer
Answer: 3% p.a
P1 = 600, r1 = ?, t1 = 5, P2 = 500, r2 = 6, t2 = 3 years, SI1 = SI2
$\frac{\text{600 x r1 x 5}}{100} =\frac{\text{500 x 6 x 3}}{100}$
r1 = 3
Hence the rate of interest = 3% p.a
- A person takes a loan of Rs. 1000 with SI for certain number of years which is same as the rate of interest. At the end of the time period the person pays Rs. 1640. Find the number of years for which the loan was taken.
- 5
- 6
- 7
- 8
Show the answer
Answer: 8
Let rate of interest be $x$, then number of years is $x$.
Given SI = 1640 - 1000 = 640, P = 1000, r= t = $x$
640 =$\frac{\text{1000 x } x \text{ x } x}{100}$
$x^2$ = 64
x = 8 years.
Hence, the loan was taken for 8 years.
- An amount of Rs. 1000 is invested in two policies such that the interest obtained from the first policy at 3% pa at end of 2 years is same as the interest obtained from the second policy at 6%pa at the end of 3 years. Find the amount invested on each policy. (Assume SI)
- Rs. 750 and Rs. 250
- Rs. 800 and Rs. 100
- Rs. 650 and Rs. 350
- Rs. 500 and Rs. 400
Show the answer
Answer: Rs. 750 and Rs. 250
Let the amount invested in first policy be $x$. Then the amount invested in second policy will be 1000-$x$.
Since the interest generated on both the policies is same,
$\frac{x\text{ x 3 x 2}}{100}$ = $\frac{(1000-x)\text{ x 6 x 3}}{100} $
=> 2$x$ = 6000 - 6$x$
=> x = 750.
Hence, the amount invested in each policy is Rs. 750 and Rs. 250
- An amount of Rs. 600 is invested for 6 months and another amount of Rs.1200 is invested for 12 months at the same rate of interest. If the interest obtained from both the investments is Rs. 135. Find the rate of interest.
- 7% p.a
- 8% p.a
- 9% p.a
- 5% p.a
Show the answer
Answer: 9% p.a
Let the rate of interest be r. Then, interest obtained on Rs. 600 for half of the year + Interest obtained on Rs. 1200 for full year is equal to 135. i.e,
$\frac{600\text{ x r x 1}}{2\text{ x }100}$ + $\frac{1200\text{ x r x 1}}{100} $ = 135
3r + 12r = 135
r = 9%
Hence the rate of interest is 9% p.a
- Anil has taken a loan Rs. 5400 at SI. At the end of 2 years he clears the loan by a paying a sum of Rs. 6696. Find the rate of interest per annum.
- 3% p.a
- 6% p.a
- 9% p.a
- 12% pa
Show the answer
Answer: 12% pa
Interest paid by Anil at the end of 2 years is 6696 - 5400 = 1296. If the rate of interest is r, then
1296 = $\frac{5400\text{ x 2 x r}}{100}$
1296 = 108r
r = 12% p.a
- Ram borrows an amount of Rs. 5000 for 4 years at 12% p.a SI and lends Rs. 2000 to chaitanya at 15% p.a and the remaining amount to advith at 10% p.a for the same time period. How much does the does gain or lose?
- No gain or loss
- Rs. 200 gain
- Rs. 200 loss
- Rs. 300 gain
Show the answer
Answer: No gain or loss
Interest on the borrowed amount = $\frac{5000\text{ x 12 x 4}}{100}$ = Rs. 2400
Interest on the lent amount = $\frac{2000\text{ x 15 x 4}}{100}$+$\frac{3000\text{ x 10 x 4}}{100}$ = Rs. 2400
Hence, Ram neither gains nor loses.
- Rate of interest on a sum of money is 4% for the first 2 years, 6% p.a for the next 2 years and 8% p.a for the remaining years. If the total interest paid by a person on a sum of Rs. 1000 is Rs. 340. After how many years did he pay the amount?(Assume SI)
- 5.75 years
- 3.25 years
- 4.5 years
- 6 years
Show the answer
Answer: 5.75 years
Let the remaining number of years be t. Now, in SI the principal remains same for every year. Hence,
$\frac{1000\text{ x 4 x 2}}{100}$ + $\frac{1000\text{ x 6 x 2}}{100}$ + $\frac{1000\text{ x 8 x t}}{100}$ = 360
80 + 120 + 80t = 340
t = $\frac{7}{4}$ = 1.75 or 1 year and 9 months
Hence, the person pays the interest after 2 + 2 + 1.75 = 5.75 or 5 years and 9 months
