The compound interest on Rs 30000 at 8 per annum is Rs 4992 the period (in years) is
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The compound interest on a certain sum of money at 6% for a period of 2 years is Rs. 8652. What is the SI on this sum if the rate is halved, and time doubled? Show
A Rs. 8400. B Rs. 8500. C Rs. 8300. D Rs. 8600. Soln. The shortcut formula is CI = Pr(r + 200)/10000. Putting CI = 8652, r = 6, we get 8652 = ${P × 6 × (6 + 200)}/10000$. We can solve it to get P = Rs. 70000. The SI = P × (2 × t) × (r / 200) = P × t × (r / 100). Putting t = 2, r = 6 and P = 70000, we get SI = Rs. 8400. Solution | Discuss! | Chapters» Question 2How much interest does an amount of Rs. 30000 earn @8% compounded annually for 2 years? A Rs. 4992. B Rs. 5092. C Rs. 4892. D Rs. 5192. Soln. Amount A = 30000 × $(1 + 8/100)^2$, which equals 30000 × $108/100$ × $108/100$ = 3 × 108 × 108 = Rs. 34992. So interest = A - P = 34992 - 30000 = Rs. 4992. Solution | Discuss! | Chapters» Question 3The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 28. What is the rate p.a. if principal is Rs. 70000? A 2%. B 4%. C 3%. D 5%. Soln. If d is the difference, r is the rate and P is the principal, then the shortcut formula for the difference between compound and simple interest over a period of 2 years is d = P × $(r/100)^2$. So rate = 100 × $√{d/P}$ = 100 × $√{28/70000}$ = 2%. Solution | Discuss! | Chapters» Question 4An amount P is invested for 1 year @2% p.a. The simple interest is Rs. 3000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually? A Rs. 3000. B Rs. 3100. C Rs. 2900. D Rs. 3200. Soln. The compound interest and simple interest are exactly same for a period of 1 year if P and r are always same. Solution | Discuss! | Chapters» Question 5An amount P is invested for 2 years @7% p.a. The simple interest is Rs. 6000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually? A Rs. 6210. B Rs. 6310. C Rs. 6110. D Rs. 6410. Soln. Let SI, P, r, t have usual meanings. Then, for 2 years, SI = (P × r × 2)/100. So P = $(50 × SI)/r$. The compound interest for 2 years by shortcut formula is ${P × r × (200 + r)}/10000$. Putting P here, it becomes, ${{(50 × SI)/r} × r × (200 + r)}/10000$ = ${SI × (r + 200)}/200$ = ${6000 × (7 + 200)}/200$ = Rs. 6210. A. 2 B. $$2\frac{1}{2}$$ C. 3 D. 4 Answer: Option A Solution(By Examveda Team)$$\eqalign{ & {\text{Amount}} = Rs.\,\left( {30000 + 4347} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,34347 \cr & {\text{Let}}\,{\text{the}}\,{\text{time}}\,{\text{be}}\,n\,{\text{years}} \cr & {\text{Then}},30000\,{\left( {1 + \frac{7}{{100}}} \right)^n} = 34347 \cr & \Rightarrow {\left( {\frac{{107}}{{100}}} \right)^n} = \frac{{34347}}{{30000}} = \frac{{11449}}{{10000}} = {\left( {\frac{{107}}{{100}}} \right)^2} \cr & \therefore n = 2\,{\text{years}} \cr} $$Isha Sharma said: (May 9, 2015) Guys this is simple divide numerator and denominator by 3 you will get your answer. Trilok said: (Sep 14, 2015) 11449/10000 = (107/100)^n , 1.1442 = (1.07)^n. We can write as log 1.1442 = n log 1.07, n = log 1.1442/log 1.07 = 0.058501/0.029383 = 2 (as per scientific calculator). Bhabani said: (Oct 20, 2015) A sum becomes double in ten years in C.I. So in how many years the principal would be 8 times? Leo said: (Nov 28, 2015) Can anyone explain me the simplification of (107/100)2? Abhilok said: (Dec 6, 2015) 2 times in 10 years. Let power = n. Dearlie Beloved said: (Dec 30, 2015) Shortcut through using ln: t = ln (34 347/30 000)/ln (1.07). Anurag Nath said: (May 12, 2016) @Hitendra. (107/100)n = 11449/10000. Therefore n=2. France said: (Jun 28, 2016) 107 * 107 is 11449 and 100 * 100 = 10000 but how is it equal to 34347/30000 ? Rkh said: (Nov 14, 2016) What if the power is( 107/100)^4?. How can we find quad root of a number? Chloe said: (Mar 27, 2017) Use the formula n = [ log(fv/p) ] / [ log (1+i)]. Where n = [ log ( 34,347/30,000) ] / [ log (1+0.07)]. B. Tatung said: (May 9, 2017) How come 3 divided by both numerator and denominator? Please, someone, explain me. Akash Kumar Sinha said: (Jul 14, 2017) 1st year CI= 7% OF 30000 ie 2100. Priya said: (Jul 29, 2017) What is 107/100? I can't understand, please explain. Shipra said: (Aug 2, 2017) Thanks people. It helped a lot! Subramanyam said: (Aug 23, 2017) Thanks, friends. It helped a lot! Narsim Bari said: (Feb 27, 2018) 30000*7/100 = 2100 for 1rst year. Now, cross-check the given calculated amount given in the question itself i.e 4347 rupees by adding 2 years amount (2100+2247)=4347. In what time the compounded interest on Rs 30000 at 7% per annum for a certain time is Rs 4347?⇒n=2 years.
What is the compound interest on Rs 31250 at 8% per annum for 2 years?=38637−31250=Rs. 7387.
What will be the compound interest on 30000?The compound interest on₹30000 at 8% per annum is ₹4992.
What is the compound interest on rupees 5000 for 3 years at 8% per annum?Hence, the correct answer is Rs. 1,653. Was this answer helpful?
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