The compound interest on a sum of Rs. 64000 at 5% per annum for a certain period is Rs. 4921, while the interest is compounded half-yearly. What will be the compound interest on the same sum at the same rate for the same period, if the interest is compounded annually?
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Answer (Detailed Solution Below)Option 2 : Rs. 4880 Free SSB Head Constable Full Mock Test 100 Questions 100 Marks 120 Mins Given: Principal = Rs. 64000 Compound Interest = Rs. 4921 Rate = 5% Concept used: When the sum is compounded half-yearly, then the rate of interest becomes half and time becomes double. Formula used: A = P(1 + R/100)T C.I = A - P A = P + C.I Where, A = Amount, P = Principal, T = Time, C.I = Compound interest and R = rate of interest Calculation: A = P + C.I ⇒ A = 64000 + 4921 = Rs. 68921 According to the question, Compounded half-yearly, A = P(1 + R/100)T ⇒ 68921 = 64000[1 + 5/(2 ×100)]2T ⇒ 68921/64000 = (41/40)2n ⇒ (41/40)3 = (41/40)2n ⇒ 2n = 3 ⇒ n = 3/2 Annual Now, compounded annually P = Rs. 64000 n = 3/2 = \({1\frac{1}{2}}\) years, and r = 5% A = P(1 + R/100)T ⇒ A = 64000(1 + 5/100)\({1\frac{1}{2}}\) ⇒ A = 64000(1 + 5/100)1 × (1 + 5/100)1/2 ⇒ A = 64000 × (1 + 5/100)(1 + 5/2 × 100) ⇒ A = 64000 × 21/20 × 41/40 = Rs. 688,80 C.I = A - P ⇒ C.I = 68880 - 64000 = Rs. 4880 ∴ The compound interest is Rs. 4880. Latest SSB Head Constable Updates Last updated on Sep 29, 2022 The Sashastra Seema Bal (SSB) is soon going to release the official notification for the SSB Head Constable Recruitment 2022. The SSB has released a total of 115 vacancies for the last recruitment cycle and this year the vacancies are expected to be released more. The SSB Head Constable Selection Process comprises four stages namely Physical Efficiency Test & Physical Standard Test, Written Examination, Skill Test/Typing Test, and Documentation and Detailed Medical Examination. With an expected salary range between Rs. 25,500 to Rs. 81,100, this is a great opportunity for candidates who wants to join the defence sector. Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now! Solution : Let the time be ` n`<br>Principal `P=Rs. 64000`<br>Amount `A=Rs. 68921`<br>Rate `R=5% `per annum or `5/2` per half-yearly<br>`A=P{1+R/(2times100)}^n`<br>`68921=64000(1+5/200)^(2n)`<br>`68921/64000=(41/40)^(2n)`<br>`(41/40)^3=(41/40)^(2n)`<br>On comparing both the sides, we get:<br>`3=2n`<br>`n=3/2years=1 1/2 `years<br>`therefore` The time `=1 1/2` years. The compound interest on a sum of Rs. 64000 at 5% per annum for a certain period is Rs. 4921, while the interest is compounded half-yearly. What will be the compound interest on the same sum at the same rate for the same period, if the interest is compounded annually?
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Answer (Detailed Solution Below)Option 2 : Rs. 4880 Free SSB Head Constable Full Mock Test 100 Questions 100 Marks 120 Mins Given: Principal = Rs. 64000 Compound Interest = Rs. 4921 Rate = 5% Concept used: When the sum is compounded half-yearly, then the rate of interest becomes half and time becomes double. Formula used: A = P(1 + R/100)T C.I = A - P A = P + C.I Where, A = Amount, P = Principal, T = Time, C.I = Compound interest and R = rate of interest Calculation: A = P + C.I ⇒ A = 64000 + 4921 = Rs. 68921 According to the question, Compounded half-yearly, A = P(1 + R/100)T ⇒ 68921 = 64000[1 + 5/(2 ×100)]2T ⇒ 68921/64000 = (41/40)2n ⇒ (41/40)3 = (41/40)2n ⇒ 2n = 3 ⇒ n = 3/2 Annual Now, compounded annually P = Rs. 64000 n = 3/2 = \({1\frac{1}{2}}\) years, and r = 5% A = P(1 + R/100)T ⇒ A = 64000(1 + 5/100)\({1\frac{1}{2}}\) ⇒ A = 64000(1 + 5/100)1 × (1 + 5/100)1/2 ⇒ A = 64000 × (1 + 5/100)(1 + 5/2 × 100) ⇒ A = 64000 × 21/20 × 41/40 = Rs. 688,80 C.I = A - P ⇒ C.I = 68880 - 64000 = Rs. 4880 ∴ The compound interest is Rs. 4880. Latest SSB Head Constable Updates Last updated on Sep 29, 2022 The Sashastra Seema Bal (SSB) is soon going to release the official notification for the SSB Head Constable Recruitment 2022. The SSB has released a total of 115 vacancies for the last recruitment cycle and this year the vacancies are expected to be released more. The SSB Head Constable Selection Process comprises four stages namely Physical Efficiency Test & Physical Standard Test, Written Examination, Skill Test/Typing Test, and Documentation and Detailed Medical Examination. With an expected salary range between Rs. 25,500 to Rs. 81,100, this is a great opportunity for candidates who wants to join the defence sector. Ace your Interest preparations for Compound Interest with us and master Quantitative Aptitude for your exams. Learn today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Open in App Solution The correct option is A 112 yearsHere, Principal P = Rs. 64000, Amount A = Rs 68921, rate R=5% per annum. Since the interest is compounded half - yearly. ∴A=P(1+R200)2n ⇒68921=64000(1+5200)2n ⇒6892164000=(4140)2n ⇒(4140)3=(4140)2n Since the base are same, equating the powers we get ⇒3=2n ⇒n=32 years=112yearsWhat rate percent will a sum of 64000 be compounded to 68921 in 3 years?64000`<br>Amount `A=Rs. 68921`<br>Rate `R=5% `per annum or `5/2` per half-yearly<br>`A=P{1+R/(2times100)}^n`<br>`68921=64000(1+5/200)^(2n)`<br>`68921/64000=(41/40)^(2n)`<br>`(41/40)^3=(41/40)^(2n)`<br>On comparing both the sides, we get:<br>`3=2n`<br>`n=3/2years=1 1/2 `years<br>`therefore` The time `=1 1/2` years. At what rate percent will a sum of Rs 640 be compounded to Rs 774.40 in two years?Answer : 10% p.a. At what rate percent will a sum of Rupees 640 be compounded?∴ Rate =10% p.a. At what rate will a sum of 3200 produce and interest of 672 in 2 years if compounded annually?This is an Expert-Verified Answer Hence, the rate is 10% per annum. What rate percent will a sum of rupees 64000 be compounded to 68921 in 3 years?64000`<br>Amount `A=Rs. 68921`<br>Rate `R=5% `per annum or `5/2` per half-yearly<br>`A=P{1+R/(2times100)}^n`<br>`68921=64000(1+5/200)^(2n)`<br>`68921/64000=(41/40)^(2n)`<br>`(41/40)^3=(41/40)^(2n)`<br>On comparing both the sides, we get:<br>`3=2n`<br>`n=3/2years=1 1/2 `years<br>`therefore` The time `=1 1/2` years.
In what time will Rs 64000 amount to Rs 68921 at 5% per annum compounded half yearly?Hence The required time is 121Years. Was this answer helpful?
At what rate per cent will a sum of 64000 be compounded?∴ Rate is 2. 5%.
At what rate per cent will a sum of 640 be compounded to 774.40 in two?At what rate per cent per annum will Rs 640 amount to 774.40 in 2 years when compounded annually? UPLOAD PHOTO AND GET THE ANSWER NOW! Answer : 10% p.a.
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At what rate per cent will a sum of ₹ 64000 be compounded to ₹ 68921 in 3 years?
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