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Principal (P) = Rs 2000 Amount (A) = Rs 2315.25 Period (n) = 3 years Let the rate of interest be r% p.a. WKT A / P = {1 + (r / 100)}n 2315.25 / 2000 = {1 + (r / 100)}3 {1 + (r / 100)}3 = (231525) / (100 × 2000) On calculating, we get, \{1+(\mathrm{r} / 100)\}^{3} = 9261 / 8000 \{1+(\mathrm{r} / 100)\}^{3} = (21 / 20)3 We get, 1 + (r / 100) = 21 / 20 r / 100 = (21 / 20) – 1 r / 100 = 1 / 20 We get, r = 100 / 20 r = 5 Therefore, rate of interest = 5% p.a. Free Nội dung chính Show
ICAR Technician: General Knowledge Free Mock Test 10 Questions 10 Marks 8 Mins Given: Compound interest on Rs.2000 for 3 years = Rs.315.25 Formulas used: Amount = Principal + Interest Amount = P(1 + r/100)n Calculation: Amount = 2000 + 315.25 = Rs.2315.25 Amount = P(1 + r/100)n ⇒ 2315.25 = 2000(1 + r/100)3 ⇒ 231525/200000 = (1 + r/100)3 ⇒ ∛9261/8000 = 1 + r/100 ⇒ 21/20 - 1 = r/100 ⇒ (21 - 20)/20 = r/100 ⇒ 1/20 = r/100 ⇒ 1 = r/5 ⇒ r = 5 ∴ The rate of interest is 5% per annum. Latest ICAR Technician Updates Last updated on Sep 22, 2022 ICAR Technician DV schedule and admit card released for various locations. The CAR Technician recruitment.is ongoing for 641 vacancies. The candidates who had qualified the Computer Based Test have been shortlisted for the Document Verification. The ICAR Technician salary will be in the pay scale of INR 21700 - INR 69,100 Ace your Interest preparations for Compound Interest with us and master Quantitative Aptitude for your exams. Learn today! Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly. Let the rate percent per annum be R. Solution : Given:<br>Principle `(P)=Rs.2000`<br>Amount `(A)=Rs.2315.25`<br>`n=1.5` years means `3` half-years.<br>The rate has to be calculated half-yearly, therefore let `R` be the rate of half-yearly.<br>As we know that,<br>`A=P(1+R/100)^n`<br>`therefore 2315.25=2000(1+R/100)^3`<br>`2315.25/2000=(1+R/100)^3`<br>`231525/2000times100=(1+R/100)^3`<br>`9261/8000=(1+R/100)^3`<br>`(21/20)^3=(1+R/100)^3`<br>`21/20=1+R/100`<br>`21/20-1=R/100`<br>`(21-20)/20=R/100`<br>`1/20=R/100`<br>`R=100/20`<br>`R=5%`.<br>Hence, the rate will be `5%` half yearly and `10%` yearly. Nội dung chính Show
More solved problems on compound interest using formula are shown below. 1. The simple interest on a sum of money for 3 years at 6²/₃ % per annum is $ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?Solution: Given, SI = $ 6750, R = \(\frac{20}{3}\)% p.a. and T = 3 years. sum = 100 × SI / R × T = $ (100 × 6750 × ³/₂₀ × 1/3 ) = $ 33750. Now, P = $ 33750, R = \(\frac{20}{3}\)% p.a. and T = 3 years. Therefore, amount after 3 years = $ {33750 × (1 + (20/3 × 100)}³ [using A = P (1 + R/100)ᵀ] = $ (33750 × 16/15 × 16/15 × 16/15) = $ 40960. Thus, amount = $ 40960. Hence, compound interest = $ (40960 - 33750) = $ 7210. 2. The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.Solution: Let the sum be $ 100. Then, SI = $ (100 × 6 × 2/100) = $ 12 and compound interest = $ {100 × (1 + 6/100)² - 100} = $ {(100 × 53/50 × 53/50) - 100} = $ (2809/25 - 100) = $ 309/25 Therefore, (CI) - (SI) = $ (309/25 – 100) = $ 9/25 If the difference between the CI and SI is $ 9/25, then the sum = $ 100. If the difference between the CI and SI is $ 18, then the sum = $ (100 × 25/9 × 18 ) = $ 5000. Hence, the required sum is $ 5000. Alternative method Let the sum be $ P. Then, SI = $ (P × 6/100 × 2) = $ 3P/25 And, CI = $ {P × (1 + 6/100)² - P} = $ {(P × 53/50 × 53/50) - P} = $ (\(\frac{2809}{2500}\)P - P) = $ (309P/2500) (CI) - (SI) = $ (309P/2500 – 3P/25) = $ (9P/2500) Therefore, 9P/2500 = 18 ⇔ P = 2500 × 18/9 ⇔ P = 5000. Hence, the required sum is $ 5000. 3. A certain sum amounts to $ 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.Solution: Let the sum be $ 100. Then, amount = $ {100 × (1 + 8/100)²} = $ (100 × 27/25 × 27/25) = $ (2916/25) If the amount is $ 2916/25 then the sum = $ 100. If the amount is $ 72900 then the sum = $ (100 × 25/2916 × 72900) = $ 62500. Hence, the required sum is $ 62500. Alternative method Let the sum be $ P. Then, amount = $ {P × (1 + 8/100)²} = $ {P × 27/25 × 27/25} = $ (729P/625) Therefore, 729P/625 = 72900 ⇔ P = (72900 × 625)/729 ⇔ P = 62500. Hence, the required sum is $ 62500. 4. In this question the formula is when the interest is compounded annually to solve this problem on compound interest. 4. At what rate per cent per annum will Ron lends a sum of $2000 to Ben. Ben returned after 2 years $2205, compounded annually?Solution: Let the required rate be R% per annum. Here, A = $ 2205, P = $ 2000 and n = 2 years. Using the formula A = P(1 + R/100)ⁿ, 2205 = 2000 × ( 1 + R/100)² ⇒ (1 + R/100)² = 2205/2000 = 441/400 = (21/20)² ⇒ ( 1 + R/100) = 21/20 ⇒ R/100 = (21/20 – 1) = 1/20 ⇒ R = (100 × 1/20) = 5 Hence, the required rate of interest is 5% per annum. 5. A man deposited $1000 in a bank. In return he got $1331. Bank gave interest 10% per annum. How long did he kept the money in the bank?Solution: Let the required time be n years. Then, amount = $ {1000 × (1 + 10/100)ⁿ} = $ {1000 × (11/10)ⁿ} Therefore, 1000 × (11/10)ⁿ = 1331 [since, amount = $ 1331 (given)] ⇒ (11/10)ⁿ = 1331/1000 = 11 × 11 × 11/ 10 × 10 × 10 = (11/10)³ ⇒ (11/10)ⁿ = (11/10)³ ⇒ n = 3. Thus, n = 3. Hence, the required time is 3 years. ● Compound Interest Compound Interest Compound Interest with Growing Principal Compound Interest with Periodic
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on Uniform Rate of Growth and Depreciation Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. At what rate per annum will Rs 2000 becomes Rs 2205 in 2 years compounded annually?∴ Rate =5% half yearly or 10% p.a. Q. A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually. At what rate percent per annum will a sum of PHP 2000 amount to PHP 2205 in 2 years compounded annually?⟹r=0. 05=5% At what rate percent per annum will a sum of rupees 2000 amount to rupees?Hence, the rate of interest will be equal to 5%. At what rate percent of compound interest will 625 become 784 in 2 years?∴R=100×325=4×3=12% At what rate percent per annum will a sum of ₹ 2000 amount to ₹ 2205 in 2 years compounded annually?Hence, the required rate of interest is 5%. Was this answer helpful? At what rate percent per annum of compound interest will Rs 2000 amounts to Rs 2332.8 in 2 years?This is Expert Verified Answer Given, Principal = 2000, A = 2332.80, Time n = 2 years. ⇒ r = 8. Therefore, R = 8%. At what rate percent per annum will a sum of Rs 2000 amount to?Hence, the rate of interest will be equal to 5%. In what time will Rs 2000 amounts to Rs 2315.25 at 5% per annum compounded annually?Given A = 2000, P = 2315.25, n = 3 years. r = 5%. Therefore the required rate is 5% per annum. At what rate per cent will 2000 amount to 2315.25 in 3 years at compound interest?At what rate percent will ₹ 2000 amount to ₹ 2315.25 in 3 years at compound interest? Hence, the rate of interest is 5% p.a.
In what time will Rs 2000 amounts to Rs 2315.25 at 5% per annum compounded annually?So it is given to us that Rs. 2000 amounts to 2315.25 in 3 years at compound interest.
What will be compound interest on rs40 000 at 16% per annum for 1.5 years if the interest is compounded half yearly?=Rs10,388.
What will be the amount on Rs 2000 at 10% compound interest in 2 years?Detailed Solution
⇒ Rs. 420. ∴ The compound interest on ₹2000 at 10% p.a. for 2 years, compounded annually, is Rs. 420.
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At what rate percent per annum at ci will principal of 2000 amount to 2315.25 in 3 years
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