On what sum of money will the SI for 7 yr 6 months at 5% per annum be 450?

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Given:

Difference between compound interest and simple interest = Rs.450

Rate (R) = 15%

Time = 2 years

Formula used:

S.I. = (P × R × T)/100

C.I. = P(1 + R/100)T – P

The difference between S.I. and C.I. for 2 years = PR2/(100)2

Where

P → Principal

R → Rate

T → Time

Calculations:

Let the principal be Rs. P.

S.I. = (P × R × T)/100

⇒ (P × 2 × 15)/100

⇒ 3P/10

C.I. = P(1 + R/100)T – P

⇒ P × (1 + 15/100)2 – P

⇒ 529P/400 – P

⇒ 129P/400

The difference between S.I. and C.I. for 2 years = (129P/400) – 3P/10

⇒ 9P/400 = 450

⇒ P = 20000

∴ The value of the sum is Rs. 20,000.

Let the principal be Rs. P.

According to the question,

The difference between the compound interest and simple interest for 2 years = PR2/(100)2

⇒ 450 = P × 15 × 15/10000

⇒ P = Rs.20,000

∴ The value of the sum is Rs. 20,000.

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Discussion :: Simple Interest - General Questions (Q.No.4)

Vibin said: (Jun 2, 2010)
I want to know the formula for converting from percentge to years and amount to years.

Dilepkumar said: (Jul 21, 2010)
si=ptr/100 p=sum t=time r=rate of intrest

Jineesh K B said: (Nov 27, 2010)
4504.5/100=20.25 20.254=81(from option)

Ratna Prathibha said: (Jan 19, 2011)
I want to know the formula for converting from percentge to years and amount to years.

Ragu said: (Feb 3, 2011)
(10081/4504.5)=(281/94.5)=(2*2/4.5) so 4/4.5=4 (given ans)but 4/4.5=0.8888 So my doubt is how the ans was 4 years? can anyone explain me clearly?

Beni said: (Feb 25, 2011)
1. T = S.I x 100/p x r 2. 81 * 100/4.5 * 450 3. if you simplify it 4 comes as the answer.

Mahesh said: (Mar 3, 2011)
The formula is i=ptr/100 p=450 t=? r=4.5 i=81 then t=100i/pr t=(10081)/4504.5) t=4 years

Anupama said: (May 23, 2011)
t=(10081)/(4504.5) t=(2*9)/4.5 t=18/4.5 y=1800/450=4 years. So, lets dived them as 1800/450 = 4 years. Bcoz if you want to convert decimal into number just put that much zeros same as above number here in 4.5 we convert it into 450 so just put two zeros above also bcoz from fraction point we increase 2 no. so 2 zeros are der. Best of luck

Triniford said: (Jan 24, 2012)
SI=PTR/100 81=4504.5x/100 81=9*4.5 =4.05/81 =4 years

Raviteja said: (Nov 17, 2012)
@Raghu. We know that I= PTR/100 He gave I=81, p=450, R= 4.5 we have to find time (T)=? T=100I/PR (10081)/(4.5*450)= 8100/2025= 4 years got it.

Sobana said: (Feb 16, 2013)
we know that formula for calculate the N value. given data is: S.I=81. P=450. R=4.5. Formula is N=100si/pr. =10081/4504.5. =8100/2025. =4. N=4 years.

Ravimanne said: (Oct 12, 2013)
Please clarify me difference between P and I and their full form and way of usage in formula?

Rajesh said: (Oct 15, 2013)
Rs. 450 at 4.5% per year gives 20.25 rupees. So to get 81 we have to perform (81/20.25) = 4.

Vinay Tiwari said: (Mar 25, 2014)
Please tell me some basic formulas related to SI.

Sandhya said: (Jul 7, 2014)
In the question given amount as 450 but not sum as 450. We know that amount = principle(or)sum + s.i. So the ans might be 4.5.

Sameera said: (Aug 7, 2014)
Yes @Sandhya I agree your view. But here sum (or) principle is not given but he say that Rs450 to yield means we have to keep in mind that the amount never yield (produce) interest only the principle will (produce) interest; so the given amount is principle only.

Sumit said: (Aug 9, 2014)
t = ? P = Rs.450. S.I = 81. R = 4.5%. As we know : SI = PRT/100. : T = S.I100/PR. i.e: 81100/450405 = 4 yr.

Sam said: (Oct 9, 2014)
1% of 450 is 4.50. 2% of 450 is doubles the 1% 9. 4% of 450 is. 18. 0.5% of 450 is half the 1% 2.25. Total 4.5 p.a. is: 20.25. For 4 years: 4*20.25== 81.

Bhavna said: (Dec 10, 2014)
Given, S.I = 81, P = 450, R = 4.5. T = S.I100/PR. T = 81100/4504.5 (Cancel 100/450 with 5 and 81 with 9). T = 9*2/4.5. T = 18/4.5 => 180/45. T = 4 Years.

Shreyank said: (Dec 29, 2014)
Let's we gone to take an answer. 450454/100*10. So the answer came to the 81 rs. That amount we shown in question so answer is true.

RAJKUMAR said: (Aug 28, 2015)

S.I = 81, P = 450, R = 4.5. T = S.I*100/P*R. T = 81*100*10/450*45 (Cancel 100/450 with 5 and 81 AND 45 CANCEL WITH 9 AND 45 AND 10 CANCEL WITH 5). T = 9*2*2/9. T = 36/9.

T = 4 Years.

Ramu said: (Jan 29, 2016)
S.I = ptr/100. 100S.I = ptr. 100S.I/p*r = t. Here p = 450, S.I = 81, r = 4.5 substitute above we get answer.

Shruthi said: (Jul 4, 2016)
Clarify me difference between I and p.

Mona said: (Jul 8, 2016)
@Shruthi. The I is an interest which had paid for using someone's money whereas p is the principal or sum which is the amount you borrowed from someone.

Srikruthi said: (Jul 28, 2016)
p = 450,r = 4.5,i = 81,t = ? I = P * R * T/100 now we have to find t=? so, t = 100 * I/P * R. t = 100 * 81/450 * 4.5. = 100 * 81/45 * 10 * 4.5 (45 * 10 = 450). = 100 * 81/45 * 45 (4.5*10 = 45). = 36/9. t =4.

Mohammed Ashik said: (Aug 8, 2016)
100% = 450. Rs. 1% = 4.5 Rs. 4% = 18.00 Rs. 0.5% = 2.25 Rs. So 4.5% = 20.25 Rs. Hence 20.25 * 4 = 81 Rs. Ans: 4 years.

Ganesh said: (Aug 28, 2016)
They gave a number of Rs 450 so as per the formula amt = principal + interest, the amount should be subtracted from interest to get the principal but they directly takes principal as 450. Is it correct? Can anyone please clarify.

Dhamo said: (Feb 19, 2017)
Formula: SI = P * T * R/100, SI = simple interest(81), P = principal(450), T = time(?), R = rate(4.5), T = SI * 100/P * R. T = 81 * 100/450 * 4.5, T = 8100/2025. T = 4. Here s the answer.

Vinod said: (Jun 5, 2017)
Here 450is given as amount but it is taken as principle. Please Clear my confusion regarding this.

Ravula Sandeep Kumar said: (Jun 5, 2017)
I should explain clearly in this. Then time =100 * 81/450 * 4.5, = 2 * 9/4.5, = 18/4.5, = 18 * 10/45, = 18 * 2/9, = 2 * 2, = 4 years.

Aiswarya Mohan V said: (Jun 21, 2017)
Given Si=81 P=450 R=4.5 T=? We know si=PRT/100. Therefore T=si100/PR, =81100/4504.5, =8110/454.5, =812/94.5, =9*2/4.5, =18/4.5, =4.

Mahesh Senthil said: (Jun 26, 2017)
450 ---> 81-----> 4.5. 24.5 --->. 81-----> 24.5, 9 9 &----- > 81, 22 = 4.

Jayraj said: (Aug 29, 2017)
Awsome @Sameera.

Faisal Irshad said: (Sep 21, 2017)
S=p+I and t=(s/p-1)/r.

Naowaz said: (Oct 6, 2017)
Here, I = (P x r x t/100).

Rushi said: (Oct 15, 2017)
@Ragu. The steps you had done is actually like this, =(100x81)/(450x4.5) =(2x81)/(9x4.5) =(2x9)/(1x4.5) =4. You hav taken =(2x2)/(4.5) bt actually 81/9 is 9 not 2.

Anirudha said: (Nov 8, 2017)
450*4.5% = Rs 18 per year. To find time 81/18 = 4.5.

Sanjay said: (Jan 2, 2018)
We can check by options also; We know that S.I=PTR/100. A.(4503.54.5) ÷ 100=70.8, B.(45044.5) ÷ 100=81(ans) means 4years, C.(4504.54.5) ÷ 100=91.1 D.(45054.5)÷100=1001.2.

R.Varshitha said: (Mar 13, 2018)
Answer is 4.7 because; amount = 450, s.i=81, p is not given, A=P+I. P=379, t=81100/(4.5379), t=4.73.

Bishal Upadhyay said: (Jun 11, 2018)
simple as that; t = (10081)/(4504.5), = 8100/{450*45/10}, = 8100/2025, = 4.

Vamsi Reddy said: (Jun 13, 2018)
100% = 450, 4.5%*x = 81, X = 4.

Hemalatha said: (Jun 26, 2018)
The amount is 1200. The rate of interest-4.5%, Thus, amount /interest =si for a year. 1200/4.5--->20.25. Now, the interest amount 81. 81/20.25===>4years.

Vicky said: (Sep 3, 2018)
How to multiply 450*4.5 to get the answer? Please explain me to remove the decimal point.

J.JEYA SHANMUGA said: (Sep 20, 2018)
T= 100 * I/P * R. T= 100 * 81/450 * 4.5. T= 4 YEARS.

Naveen said: (Apr 2, 2019)
= 10081/4504.5, = 20*18/90, = 36/9, = 4 years (so simple).

Ayesha said: (May 27, 2019)
How P is the sum? P is principle right. A is total amount. How it will come as years?

Anand said: (Jun 13, 2019)
Thanks @Rajesh.

Prabhanshu said: (Oct 19, 2019)
In this question principal is given or amount is given since as we know amount = principal + simple interest ?

Khushi said: (Nov 13, 2019)
What is the difference between the Amount (A) and principle (P)? Please, explain!

Kimi said: (Jul 5, 2020)
@Khusi. Amount, the principal is the money which we lend for example I want to take 50 rupees from the bank so that will be loan or pricipal after 1 year the bank also want s s profit so they give a rate of interest for eg 2 pc so simple interest is prt/100 which will be 1 so at the end of the year they will have to give bank 501 rupees which is the amount. So a=si + p.

Retty said: (Oct 15, 2020)
Is amount and principal same? Please explain me.

Glory said: (Jan 17, 2021)
In that question, the amount was given but they have directly taken as principal. Why? please clarify it.

Lukman Ibrahim said: (Mar 2, 2021)
How to get 4 years? Please anyone explain.

SIDDHARTH said: (Jul 5, 2021)
S.I = P * R * T/100. So, We Get T = S.I 100/PR T = 81 * 100/450 * 4.5, So, T = 4 YEARS.

Deepak said: (Feb 26, 2022)
SI = PRT/100. PRINCIPAL = AMOUNT-SI (OR) SI100/RT.

Sherab Jatsho said: (Mar 12, 2022)
Formulae T= S.I 100÷PR derives from S.I= PRT/100. here SI is 81. And P is 450.

Dave said: (Mar 12, 2022)

Simple interest formula. S.I=(PxRxT)/100 ---------------> (1) where s.i =simple interest R=rate % P=sum or principal T=year. Amount = principal + simple interest A = P + S.I ------------> (2). From the question. S.I = 81 Amount =450 R=4,5% P=? A = P + S.I -----> (2) 450 = P + 81 p=450 - 81 =369 i.e :- P =369 And now using eq(1) S.I =(P x R xT) / 100.............(1) 81=(369 x 4.5 x T) / 100 T= (81 x 100)/369 x 4.5

T= 4 years.