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Compute the amount and the compound interest in the following by using the formulae when: Solution\[\text{ Applying the rule A = P }\left( 1 + \frac{R}{100} \right)^n \text{ on the given situations, we get: }\] The compound interest on Rs. 1,60,000 for 2 years at 10% per annum when compounded semi-annually is:
Answer (Detailed Solution Below)Option 2 : Rs. 34,481 Free RRB Group D: Memory Based Question Full Test based on 17 Aug 2022 100 Questions 100 Marks 90 Mins Given: Principal = Rs 1,60,000 Time = 2 years Rate of interest = 10% p.a compounded semi-annually Concept used: Amount = P × (1 + r/100)t When compounded semi-annually, Rate becomes half i.e R = 10%/2 = 5% And time becomes double New time T = 2 × 2 = 4 years Calculation: Now, According to the formula used A = P × (1 + R/100)T ⇒ A = 1,60,000 (1 + 5/100)4 ⇒ A = 194481 So, Compound Interest = Amount - Principal ⇒ Compound Interest = 194481 - 160000 ⇒ Compound Interest = 34,481 ∴ The required compound interest is Rs. 34481. Latest RRB Group D Updates Last updated on Sep 27, 2022 The Railway Recruitment Board has released RRB Group D Phase 5 Admit Card. The exam will be conducted on 6th and 11th October 2022 only for the RRC South Western Railway. Currently, the Phase 4 is running and this will continue till 7th October 2022. The RRB (Railway Recruitment Board) is conducting the RRB Group D exam to recruit various posts of Track Maintainer, Helper/Assistant in various technical departments like Electrical, Mechanical, S&T, etc. The selection process for these posts includes 4 phases- Computer Based Test Physical Efficiency Test, Document Verification, and Medical Test. Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now! Solution: Table of Contents
What is known: Principal, Time Period and Rate of Interest What is unknown: Amount and Compound Interest (C.I) Reasoning: A = P[1+(r/100)]n Steps: (i) P = ₹ 10800 N = 3 years R = 12(1/2)% = (25/2)% compounded annually A = P[1+(r/100)]n A = 10800[1+(25/(2×100))]3 A = 10800 (225/200)3 A = 10800 × (225/200) × (225/200) × (225/200) A = 15377.34 C.I. = A - P = 15377.34 - 10800 = 4577.34 Answer: Amount = ₹ 15377.34 Compound Interest = ₹ 4577.34 (ii) P = ₹ 18000 N = 2(1/2) years R = 10% compounded annually A = P[1+(r/100)]n Since 'n' is 2(1/2) years, amount can be calculated for 2 years and having amount as principal Simple Interest(S.I.) can be calculated for 1/2 years because C.I. is only annually A = P[1+(r/100)]n A = 18000[1+(10/100)]2 A = 18000 × (11/10) × (11/10) A = 21780 Amount after 2 years = ₹ 21870 S.I. for 1/2 years = 1/2 × 21780 × 10/100 = 1089 Amount after 2(1/2) years = 21780+1089 = ₹ 22869 C.I. after 2(1/2) years = 22869 - 18000 = ₹ 4869 Answer: Amount = ₹ 22869 Compound Interest = ₹ 4869 (iii) P = ₹ 62,500 N = 1(1/2) years R = 8% compounded half yearly A = P[1+(r/100)]n There are 3 half years in 1(1/2) years. Therefore, compounding has to be done 3 times and rate of interest will be 4%. A = P[1+(r/100)]n A = 62500[1+(4/(100)]3 A = 62500 (104/100)3 A = 62500 × (104/100) × (104/100) × (104/100) A = 70304 C.I. = A - P = 70304 - 62500 = 7804 Answer: Amount = ₹ 70304 Compound Interest = ₹ 7804 (iv) P = ₹ 8000 n = 1 year R = 9% p.a. compounded half yearly A = P[1+(r/100)]n S.I. for 1st 6 months = (1/2) × 8000 × (9/100) = 40 × 9 = 360 Amount after 1st 6 months including Simple Interest = 8000 + 360 = ₹ 8360 Principal for 2nd 6 months = ₹ 8360 S.I. for 2nd 6 months = 1/2 × 8360 × 9/100 = (418×9)/100 = 376.20 C.I. after 1 year (9% p.a. interest half yearly) = 360 + 376.20 = 736.20 Amount after 1 year (9% p.a. interest half yearly) = 8000 + 736.20 = 8736.20 Answer: Amount = ₹ 8736.20 Compound Interest = ₹ 736.20 (v) P = ₹ 10,000 n = 1 year R = 8% p.a. compounded half yearly A = P[1+(r/100)]n There are 2 half years in 1 years. Therefore, compounding has to be done 2 times and rate of interest will be 4% A = P[1+(r/100)]n A = 10000[1+(4/100)]2 A = 10000 × (104/100) × (104/100) A = 10816 C.I. after 1 year (8% p.a. interest half yearly) = 10816 - 10000 = 816 Amount after 1 year (8% p.a. interest half yearly) 10816 = 10816 Answer: Amount after 1 year = ₹ 10816 Compound Interest after 1 year = ₹ 816 ☛ Check: NCERT Solutions for Class 8 Maths Chapter 8 Video Solution: Calculate the amount and compound interest on(a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually(b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually(c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly(d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)(e) ₹ 10,000 for 1 year at 8% per annum compounded half yearlyNCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 1 The amount and compount interest are (i) ₹ 15377.34 and ₹ 4577.34 (ii) ₹ 22869 and ₹ 4869 (iii) ₹ 70304 and ₹ 7804 (iv) ₹ 8736.20 and ₹ 736.20 (v) ₹ 10816 and ₹ 816 ☛ Related Questions: Saving The power of compounding grows your savings faster 3 minutes The sooner you start to save, the more you'll earn with compound interest. Compound interest is the interest you get on:
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest. This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest. Save more with compound interestThe power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later. For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
Compound interest formulaTo calculate compound interest, use the formula: A = P x (1 + r)n A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02) n = the number of time periods How to calculate compound interestTo calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly: 1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042 2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24 3. Use the compound interest formula A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106 A = $2,211.64 Lorenzo and Sophia compare the compounding effect Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term. After five years:
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest. Answer VerifiedHint: Here we will convert the given rate and year for half-yearly as we have to find the amount for half-yearly. We will then calculate the amount accumulated during this period using the calculated rate and given principal. Then we will put these values in the formula of the Compound Interest and solve it to get the required answer. Formula Used: We will use the following formulas:1. Compound Interest = Amount – Principal2. Amount \[ = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]Here, \[P = \] Principal Amount, \[R = \] Interest Rate and \[n = \] TimeComplete step-by-step answer: The data given to us are,Principal Amount \[ = {\rm{Rs}}.160000\]…..\[\left( 1 \right)\]Rate per annum \[ = 10\% \]$\therefore $ Rate per half yearly \[ = 5\% \]….\[\left( 2 \right)\]Time \[ = 2year\]As 1 year have two half year$\therefore $ Time for half yearly \[ = 2 \times 2 = 4\] half year …..\[\left( 3 \right)\]Substituting the value from equation \[\left( 1 \right)\] and \[\left( 2 \right)\] in formula Amount\[ = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\], we getAmount \[ = 160000{\left( {1 + \dfrac{5}{{100}}} \right)^4}\]Taking LCM inside the bracket, we get\[ \Rightarrow \] Amount \[ = 160000{\left( {\dfrac{{100 + 5}}{{100}}} \right)^4}\]Adding the terms, we get\[ \Rightarrow \] Amount \[ = 160000{\left( {\dfrac{{105}}{{100}}} \right)^4}\]Dividing the terms inside the bracket, we get\[ \Rightarrow \] Amount \[ = 160000{\left( {1.05} \right)^4}\]Simplifying the equation, we get\[ \Rightarrow \] Amount \[ = {\rm{Rs}}.194481\]….\[\left( 4 \right)\]So, we get our amount as Rs. 194481.Next, we will find the Compound interest.Substituting the value from equation \[\left( 1 \right)\] and \[\left( 4 \right)\] in the formula Compound Interest = Amount – Principal, we getCompound Interest \[ = 194481 - 160000\]Subtracting the terms, we get\[ \Rightarrow \] Compound Interest \[ = \] Rs. 34481Therefore, the amount after the compound interest of Rs. 34481 on the principal amount Rs. 160000 for 2 years at 10% per annum compounded half-yearly is Rs. 1994481. Note: Compound interest is calculated on the principal amount plus the interest in the previous year. It is because of the reinvestment of interest rather than paying it out. Compound interest increases the money at such a rate that it is sometimes also known as exponential growth. The compound Interest can be calculated monthly or per day as well and is often called interest on interest.What would be the compound interest on INR 160000 at 15% per annum for 2 years 4 months compounded annually?194481 - Rs. 160000=Rs. 34481.
What is the compound interest on rupees 20000 at 10% for 2 years?Where P is principal, R is rate of interest and T is time. ∴ The compound interest for 2 years is Rs. 2464.
In what time will ₹ 160000 become ₹ 194481 if interest is 10% per annum compounded semi annually?Answer: Time (n) = 2 years.
What is the interest earned on Rs 1000 for 2 years at 10% per annum compound interest compounded annually?∴ The Interest Amount will be Rs. 210.
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Find the compound interest on Rs 160000 at 10% per annum for 2 years compounded half-yearly
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