Installment

 Problem : 1 [ Installment ]       Solve this type of problem 1. A briefcase is available for Rs 800 cash or for Rs 500 cash down payment and Rs 320 to be paid after 6 months. Find the rate of interest charged under the installment plan. Show Answer A: Cash Price = 800Down Payemnt = 500Remaining Balance = 800 - 500 = 300The installment to be paid at the end of 6 months = 320:. the interest charged on Rs 300, for a period of 6 months = Rs 320 - Rs 300 = 20If R % is the rate of interest per annum, then (300 × R × 6) / (100 × 12) = 20R = 13.3333Thus, the rate of interest charged under the installment paln is = 13.3333 per annum

 Problem : 2 [ Installment ]       Solve this type of problem 2. A bicycle is sold for Rs 1800 cash or for Rs 600 cash down payment followed by 2 monthly installmnets of Rs 610 each. Compute the rate of the interest charged under the installment scheme. Show Answer A: Cash Price = 1800Down Payemnt = 600Number of Installment = 2Installment Amount = 610Remaining Balance = 1800 - 600 = 1200After 2 months Amount = 1200 + 1200 × 2 / 12 × R / 100 = 1200 + (2400 × R) / 1200  = 1200 + 2 × R ->(1)1^(st) Installment = 610 + (610 × R × 1) / (12 × 100)Total Installment = 610 × 2 + (610 × R × (1)) / (12 × 100) = 1220 + (610 × R × (1)) / 1200 = 1220 + 61/120 × R ->(2)From (1) and (2) 1200 + 2 × R = 1220 + 61/120 × R2 × R - 61/120 × R = 1220 - 1200179/120 × R = 20R = 2400/179:. R = 2400/179OR METHODCash Price = 1800Down Payemnt = 600Number of Installment = 2Installment Amount = 610Remaining Balance = 1800 - 600 = 1200Total Installment = 610 × 2 = 1220Interest = 1220 - 1200 = 20 ->(1)Principal for 1^(st) month = 1200Principal for 2^(nd) month = 590Total = 1790:. Installment = (1790 × R × 1) / (100 × 12) ->(2)From (1) and (2)(1790 × R × 1) / (100 × 12) = 20R = (20 × 100 × 12) / 1790R = 2400/179

 Problem : 3 [ Installment ]       Solve this type of problem 3. A washing machine is available at Rs 6400 cash or for Rs 1400 cash down payment and 5 monthly installments of Rs 1030 each. Calculate the rate of interest charged under the instalment plan. Show Answer A: Cash Price = 6400Down Payemnt = 1400Number of Installment = 5Installment Amount = 1030Remaining Balance = 6400 - 1400 = 5000After 5 months Amount = 5000 + 5000 × 5 / 12 × R / 100 = 5000 + (25000 × R) / 1200  = 5000 + 125/6 × R ->(1)1^(st) Installment = 1030 + (1030 × R × 4) / (12 × 100)2^(nd) Installment = 1030 + (1030 × R × 3) / (12 × 100)3^(rd) Installment = 1030 + (1030 × R × 2) / (12 × 100)4^(th) Installment = 1030 + (1030 × R × 1) / (12 × 100)Total Installment = 1030 × 5 + (1030 × R × (4 + 3 + 2 + 1)) / (12 × 100) = 5150 + (1030 × R × (10)) / 1200 = 5150 + 103/12 × R ->(2)From (1) and (2) 5000 + 125/6 × R = 5150 + 103/12 × R125/6 × R - 103/12 × R = 5150 - 500049/4 × R = 150R = 600/49:. R = 600/49OR METHODCash Price = 6400Down Payemnt = 1400Number of Installment = 5Installment Amount = 1030Remaining Balance = 6400 - 1400 = 5000Total Installment = 1030 × 5 = 5150Interest = 5150 - 5000 = 150 ->(1)Principal for 1^(st) month = 5000Principal for 2^(nd) month = 3970Principal for 3^(rd) month = 2940Principal for 4^(th) month = 1910Principal for 5^(th) month = 880Total = 14700:. Installment = (14700 × R × 1) / (100 × 12) ->(2)From (1) and (2)(14700 × R × 1) / (100 × 12) = 150R = (150 × 100 × 12) / 14700R = 600/49

 Problem : 4 [ Installment ]       Solve this type of problem 4. A computer is sold by a company for Rs 19200 cash or for Rs 4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12 % per annum, find each installment. Show Answer A: Cash Price = 19200Down Payemnt = 4800Number of Installment = 5Rate = 12Remaining Balance = 19200 - 4800 = 14400At the end of 5 months, Amounts to = 14400 + (14400 × 5 × 12) /(12 × 100) = 14400 + 720 = 15120 ->(1) Let Installment = X 1^(st) Installment = X + (12 × X × 4) / (12 × 100)2^(nd) Installment = X + (12 × X × 3) / (12 × 100)3^(rd) Installment = X + (12 × X × 2) / (12 × 100)4^(th) Installment = X + (12 × X × 1) / (12 × 100)Total Installment = X + ( X + (12 × X × 4) / (12 × 100) ) + ( X + (12 × X × 3) / (12 × 100) ) + ( X + (12 × X × 2) / (12 × 100) ) + ( X + (12 × X × 1) / (12 × 100) )Total Installment = 5 X + (12 × X ×(4 + 3 + 2 + 1))/ (12 × 100)Total Installment = 5 X + 1/10 × XTotal Installment = 51/10 X ->(2)From (1) and (2) 51/10 X = 15120X = (15120) / (51/10)X = 50400/17:. Installment Amount = 50400/17OR METHODCash Price = 19200Down Payemnt = 4800Number of Installment = 5Rate = 12Remaining Balance = 19200 - 4800 = 14400Let Installment = X:. Interest Paid = 5 X - 14400 ->(1)Principal for 1^(st) month = 14400Principal for 2^(nd) month = 14400 - 1 XPrincipal for 3^(rd) month = 14400 - 2 XPrincipal for 4^(th) month = 14400 - 3 XPrincipal for 5^(th) month = 14400 - 4 XTotal = 72000 - 10 X:. Interest = ((72000 - 10 X) × 12 × 1) / (100 × 12) ->(2):. From (1) and (2)((72000 - 10 X) × 12 × 1) / (100 × 12) = 5 X - 14400(72000 - 10 X) = 500 X - 1440000500 X + 10 X = 72000 + 1440000510 X = 1512000:. X = 50400/17

 Problem : 5 [ Installment ]       Solve this type of problem 5. A State Government announces sale of flats of Rs 555000 cash or Rs 42750 cash down payment and 3 equal Yearly installments. The Government also charges a nominal interest at the rate of 8 % per annum copuounded as installment plan in this welfare scheme. If one purchases a flat under this installment plan, calculate the value of each installment. Show Answer A: Cash Price = 555000Down Payemnt = 42750Number of Installment = 3Rate = 8Remaining Balance = 555000 - 42750 = 512250 Let Installment = X Now present value of amount of X Rs paid at the end of 1st Year  = X / ( 1 + 8/100 ) = X × 25/27Similarly, for 2^(nd) Year = X × (25/27)^2Similarly, for 3^(rd) Year = X × (25/27)^3:. The total of the present values of the 3 Installment is Rs ( X × 25/27 + X × (25/27)^2 + X × (25/27)^3 )and this must be equal to 512250:. ( X × 25/27 + X × (25/27)^2 + X × (25/27)^3 ) = 512250:. X ( 50725/19683 ) = 512250X = 403304670/2029:. Installment Amount = 403304670/2029Total Amount Paid = 403304670/2029 × 3 = 1209914010/2029Interest = Total Paid - Balance Amount = 1209914010/2029 - 512250 = 170558760/2029

 Problem : 6 [ Installment ]       Solve this type of problem 6. A man borrows money from a finance company and has to pay it back in 2 equal Half Yearly installments of Rs 4945 each. If the interest is charged by the finance company at the rate of 15 % per annum compounded as installment plan, find the principal and the total interest paid. Show Answer A: InstallAmt = 4945Number of Installment = 2Rate = 7.5The amount of 4945 Rs paid at the end of 1st Year has its principal equal to  = 4945 / ( 1 + 7.5 / 100 ) = 4945 / ( 107.5 / 100 ) = 4945 × 0.9302Similarly, for 2^(nd) Year = 4945 × (0.9302)^2:. The total of the present values of the 2 Installment is Rs ( 4945 × 0.9302 + 4945 × (0.9302)^2 ) = 8879.0698Total Amount Paid = 4945 × 2 = 9890Interest = Total Paid - Balance Amount = 9890 - 8879.0698 = 1010.9302

 Problem : 7 [ Installment ]       Solve this type of problem 7. A TV set is available for Rs 19650 cash payment or for Rs 3100 cash down payment and 3 equal Yearly installments. If the shopkeeper charges interest at the rate of 10 % per annum compounded as installment plan, calculate the amount of each installment. Show Answer A: Cash Price = 19650Down Payemnt = 3100Number of Installment = 3Rate = 10Remaining Balance = 19650 - 3100 = 16550 Let Installment = X Now present value of amount of X Rs paid at the end of 1st Year  = X / ( 1 + 10/100 ) = X × 10/11Similarly, for 2^(nd) Year = X × (10/11)^2Similarly, for 3^(rd) Year = X × (10/11)^3:. The total of the present values of the 3 Installment is Rs ( X × 10/11 + X × (10/11)^2 + X × (10/11)^3 )and this must be equal to 16550:. ( X × 10/11 + X × (10/11)^2 + X × (10/11)^3 ) = 16550:. X ( 3310/1331 ) = 16550X = 6655:. Installment Amount = 6655Total Amount Paid = 6655 × 3 = 19965Interest = Total Paid - Balance Amount = 19965 - 16550 = 3415

 Problem : 8 [ Installment ]       Solve this type of problem 8. Ram borrowed a sum of money and returned it in 3 equal Quarterly installments of Rs 17576 each. Find the sum borrowed, if the rate of interest charged was 16 % per annum compounded as installment plan. Find also the total interest charged. Show Answer A: InstallAmt = 17576Number of Installment = 3Rate = 4The amount of 17576 Rs paid at the end of 1st Year has its principal equal to  = 17576 / ( 1 + 4 / 100 ) = 17576 / ( 104 / 100 ) = 17576 × 0.9615Similarly, for 2^(nd) Year = 17576 × (0.9615)^2Similarly, for 3^(rd) Year = 17576 × (0.9615)^3:. The total of the present values of the 3 Installment is Rs ( 17576 × 0.9615 + 17576 × (0.9615)^2 + 17576 × (0.9615)^3 ) = 48775Total Amount Paid = 17576 × 3 = 52728Interest = Total Paid - Balance Amount = 52728 - 48775 = 3953