BMS 1
Unit 1Interest and Annuity Q1) Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account today?A1)The following information is given:Future value = $5,000Interest rate = 5%Number of periods = 6We want to solve for the present value.PV = FV/ (1 + r)tInserting the known information,PV = 5,000 / (1 + 0.05) 6PV = 5,000 / (1.3401)PV = 3,731 Q2) Harpreet invests 1200rs. At 10 percent per annum for some time and it becomes 1560 then find the principal when that will become 2232 at 8 percent p.a. in the same time.A2) Here in first situation- P = 1200, A = 1560 and i = 0.10So that,In second situation-A = 2232, n = 3, i = 0.08 Q3) A sum of money invested at C.I. payable yearly amounts to 10, 816 rs. at the end of the second year and to 11,248.64 rs. at the end of the third year. Find the rate of interest and the sum.A3) Here A1 = 10,816, n = 2, and A2 = 11,248.64, n = 3We know that A = P (1 + i)n we get,10,816 = … (i)11,248.64 =… (ii)Here on dividing equation (2) by (1)-We get-And Hence the rate is 4 percent.Now from first equation-10,816 = OrNow-P = antilog 4.000 = 10,000Therefore the require answer- 10,000 Q4) Sundar decides to deposit 20,000rs. at the end of each year in a bank which pays 10% p.a. compound interest.If the installments are allowed to accumulate, what will be the total accumulation at the end of 9 years?A4) Suppose A. be the total accumulation at the end of 9 years. Then we get-Here P = 20,000 rs.,i = 10/100 = 0.1 and n = 9ThenHence the total required accumulation is 2,71,590rs. Q5) Rajeev purchased a flat valued at 3,00,000rs. He paid 2,00,000rs. at the time of purchase and agreed to pay the balance with interest of 12% per annum compounded half yearly in 20 equal half yearly installments.If the first installment is paid after six months from the date of purchase, find the amount of each installment.[Given log 10.6 = 1.0253 and log 31.19 = 1.494]A5) Here2,00,000 has been paid at the time of purchase when cost of the flat was 3,00,000, we have toconsider 20 equated half yearly annuity payment P when 12% is rate of annual interest compounded halfyearly for present value of 1,00,000rs.So that-OrThen-Hence the amount of each installment = 8,718.40Suppose,Taking log-HenceX = 0.3119 Q6) A machine valued at 500,000 depreciates at 6% per annum then in how many year its value will reduce to 100,000?A6) Here P = 500,000, r = 0.06, n = ? and the final value is = 100,000We know that-Taking log on both sides-So that-Therefore approximately it will take 26 years for the value decline to 100,000 Q7) Ayesha invests Rs. 3000 initially and then Rs. 1800 at the end of the first, second and third years and finally Rs. 600 at the end of 4th year.If the interest is paid annually at the rate of 6.5% then find the value of the investment at the end of 5th year.A7) Rs. 3000 is invested for 5 years and grows to-The three sums of Rs. 1800 are invested for 4, 3 and 2 years and grow in total-And Rs. 600 is invested for 1 year and grows to-Then the total value at the end of 5 years will be 11,280.81 Q8) A man buys a machine for Rs.20,00. What its value be after 6 years, if it is assumed to depreciate at a fixed rate of 12% per annum.A8) Here we have P = 20,000, n = 6 and r = -0.12 (rate of interest is negative in depreciation)Then,So that the value of the machine in 6 years will be = 9288.08 Q9) Find out the simple interest on 5600 rs. At 12 percent per annum from July 15 to September 26, 2020.A9) Here we calculate the time-Total days from july 15 to sept 26 = 73 days or 73/365 = 1/5 yearsAnd P = 5600, i = 12/100 = 0.12Simple interest = P.i.n. = 5600 Hence the simple interest is – 134.40 Q10) You are scheduled to receive Rs. 13,000 in two years. When you receive it, you will invest it for six more years at 8 percent per year. How much will you have in eight years?A10) We want to solve for the future value.FV = PV/ (1 + r)tInserting the known information,13,000 (1 + 0.08) 6Rs. 20,629.37
0 matching results found