Science By:Sudheer GuptaHelping Hand for Summative ...



Some Important TermsPrincipal : The money borrowed, lent or deposited in a bank for a certain period of time is called the principal or the sum.Amount : The sum total of principal and interest after a specified time is called the amount.Interest : Extra money given by the bank or borrower or given to the lender is called the interest.(a) Simple interest : In simple interest, the interest is calculated uniformly on the original principal throughout the loan perid. Using the formula:Where, S. I. = Simple InterestP = PrincipalR = Rate of interestT = Time in year(b) Compound interest : In this case, interest is calculated for a given unit of time called conversion period and then the interest is added to the previous principal to get new principal. Again interest is calculated and added is calculated and added to the principal and so on.The different interest so obtained is added to get compound interest.Rate : Rate means rate of interest which is generally specified as a percentage per year or half year.Time : The period for which money is borrowed or lent or deposited in a bank is called time. Generally time is taken in year.Example – 1. A man invests Rs. 46,875 at 4% per annum compound interest for 3 years. CalculateThe interest for the 1st year.The amount standing to his credit at the end of 2nd year.The interest for the third year. Solution : P = Rs. 46875, T = 3 years, R = 4%(i) Interest for the first year(ii) Principal for the second year = Amount after one yearInterest for the second year (iii) Principal for the second year = Rs. 50,700Interest for third year = Rs. 50,700 X 4 X 1/100 ??????????= Rs. 2028Example - 2. Simple interest on a sum of money for 2 years at 4% is 450. Find the C.I. at the same rate for 1 year if the interest is reckoned half yearly. Solution:P = ?, S.I. = Rs. 450, R = 4%p.a.T = 2 yearsP = Rs. 5625.R = 2% half yearlyCompound interest after for 1 yearExample – 3. Calculate the compound interest for the second year on Rs. 8,000 invested for 3 years at 10% p.a. Also find the sun due at the end of third year.Solution : P = Rs. 8,000, R = 10% p.a. T = 3 yearsInterest for the 1st year= Rs. 8000 X 10 X 1/100= Rs. 800Principal for the second year= Amount at the end of one year= Rs. 8000 + Rs. 800= Rs. 8800Interest for the second year= Rs. 8800 X 10 X 1/100= Rs. 880Compound interest for second year= Rs. 880Principal for the third year= Amount at the end of two years= Rs. 8800 + Rs. 880= Rs. 9680Interest for the third year= Rs. 9680 X 10 X 1/100 = Rs. 968Sum due at the end of third year= Rs. 9680 + Rs. 968= Rs. 10,648Example – 4. A man borrowed Rs.5000 at 12% C.I. per anum, interest payable every six months. He pays back Rs.1,800 at end of every six months. Calculate the third payment the he has to make at the end of 18 months in order to clear the entire loan.Solution : P = Rs. 5000, R = 12% p.a. = 6% half yearlyAmount after 1st half year= Rs. 5000 + Rs. 300 = 5300Amount paid after 1st half year = Rs. 1800Balance amount = Rs. 5300 – Rs. 1800= Rs. 3500Amount paid after 2nd half year = Rs. 1800Balance amount = Rs. 3710 – Rs. 1800= Rs. 1910Amount at the end of 3rd half year= Rs. 1910 + Rs. 114.60= Rs. 2024.60Example – 5. A man invests Rs. 5,000 for three years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 5,600. Calculate. The rate of interest per annumThe interest accrued in the second yearTthe amount at the end of third year.Solution : (i) P = Rs. 5,000, A = Rs. 5,600, T = 1 yearI = A – P = Rs. (5600 - 5000) = Rs. 600(ii) Principal for the second year = Rs. 5600(iii) Amount at the end of 2nd year = Rs. (5600 + 672) = Rs. 6272= Principal for third year Example – 6. A person invests Rs. 10,000 for two years at a certain rate of interest compounded annually. At the end of one year the sum amount to Rs. 11,200. Calculate: The rate of intersect per annumThe amount at the end of second year.Solution :(i) P = Rs.10,000, A = Rs.11,200, T = 1 yearI = A – P = Rs. (11,200 – 10,000)= Rs. 1200(ii) Principal for the second year = Rs. 11,200The amount at the end of the second year= Rs. (11,200 + 1,344)= Rs. 12,544COMPOUND INTEREST BY USING FORMULAEHere we useP = Principal, r = Rate in percentt = Time in year, A = Amountn = No. of conversion period.In case of interest is compounded half yearly Example – 1. Calculate the amount and the compound interest on a sum of Rs.30,000 at the end of 3 years at the rate of 5% p.a. compounded annually.Solution : Here, P = Rs.30000, r = 5% p.a.t = 3 year, n = 3Example - 2. Find the compound interest on Rs.160000 at 15% per annum for 2 years 4 months compounded annually.Solution: Here P = Rs.160000, r = 15% p.a.t = 2 years 4 monthsA = 2(4/12) = 2(1/3) yearsExample - 3. The simple interest on a sum of money for 2 years at 4% p.a. is Rs.450. Find the compound interest on this sum of money at the same rate of 1 year if the interest is reckoned half yearly. Solution : Here, P = ? T = 2 years, R = 4% p.a.Example - 4. What sum of money will amount to Rs.3630 in 2 years at 10% per annum compound interest?Solution : Here, P=? A = Rs.3630, r = 10% p.a.t = 2 years, n = 2A = P (1 + r/100) nRs.3630 = P(1 + 10/100)2= P(110/100)2= (121/100)PExample – 5. On a certain sum of money, the difference between the compound interest for a year, payable half yearly and the simple interest for a year is Rs.180. Find the sum lent out, the rate of interest in both the cases being 10% per annum.Solution : Let the principal P = x, t = 1 yearr = 10% p.a = 5% per conversion period,n = 2.Example – 6. A certain sum of money amounts to Rs.5292 in 2 years and to Rs.5556.60 in 3 years, interest being compounded annually. Find the rate percent and the sum.Solution : Here, r =? P = x (say)T = 2 years and 3 yearsA = Rs.5292 in 2 years and Rs.5556.60 in 3 years.using (i) Example – 7. The difference between the C.I. and S.I. on a sum of money deposited for 2 year at 5% per annum was Rs.12. Find the sum of the money.Solution : Let P = x, r = 5%, t = 2 years ................
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