Please Compute the total amount paid, monthly payment, and total interest paymen
ID: 2810659 • Letter: P
Question
Please Compute the total amount paid, monthly payment, and total interest payment for different annual interest rate level. Plot payment and total interest, and discuss how they change with respect to interest rate level. Please label points on graph if possible
Auto Loan Payment Calculator Inputs Auto Loan Amount $20,000 Annual Interest Rate 8.50% Term of Loan in Years 3 First Payment Date 2/1/18 Last Payment Date 1/1/21 Frequency of Payment Monthly Summary Number of Payments 36 Rate (per period) 0.708% Payment (per period) $631.35 Total Interest $2,728.63 Total Payments $22,728.63 No. Due Date Payment Due Additional Payment Interest Principal Balance $20,000.00 1 2/1/18 631.35 0.00 141.67 489.68 19,510.32 2 3/1/18 631.35 0.00 138.20 493.15 19,017.17 3 4/1/18 631.35 0.00 134.70 496.65 18,520.52 4 5/1/18 631.35 0.00 131.19 500.16 18,020.36 5 6/1/18 631.35 0.00 127.64 503.71 17,516.65 6 7/1/18 631.35 0.00 124.08 507.27 17,009.38 7 8/1/18 631.35 0.00 120.48 510.87 16,498.50 8 9/1/18 631.35 0.00 116.86 514.49 15,984.01 9 10/1/18 631.35 0.00 113.22 518.13 15,465.88 10 11/1/18 631.35 0.00 109.55 521.80 14,944.08 11 12/1/18 631.35 0.00 105.85 525.50 14,418.58 12 1/1/19 631.35 0.00 102.13 529.22 13,889.36 13 2/1/19 631.35 0.00 98.38 532.97 13,356.39 14 3/1/19 631.35 0.00 94.61 536.74 12,819.65 15 4/1/19 631.35 0.00 90.81 540.54 12,279.11 16 5/1/19 631.35 0.00 86.98 544.37 11,734.74 17 6/1/19 631.35 0.00 83.12 548.23 11,186.51 18 7/1/19 631.35 0.00 79.24 552.11 10,634.40 19 8/1/19 631.35 0.00 75.33 556.02 10,078.38 20 9/1/19 631.35 0.00 71.39 559.96 9,518.42 21 10/1/19 631.35 0.00 67.42 563.93 8,954.48 22 11/1/19 631.35 0.00 63.43 567.92 8,386.56 23 12/1/19 631.35 0.00 59.40 571.95 7,814.61 24 1/1/20 631.35 0.00 55.35 576.00 7,238.61 25 2/1/20 631.35 0.00 51.27 580.08 6,658.53 26 3/1/20 631.35 0.00 47.16 584.19 6,074.34 27 4/1/20 631.35 0.00 43.03 588.32 5,486.02 28 5/1/20 631.35 0.00 38.86 592.49 4,893.53 29 6/1/20 631.35 0.00 34.66 596.69 4,296.84 30 7/1/20 631.35 0.00 30.44 600.91 3,695.93 31 8/1/20 631.35 0.00 26.18 605.17 3,090.76 32 9/1/20 631.35 0.00 21.89 609.46 2,481.30 33 10/1/20 631.35 0.00 17.58 613.77 1,867.53 34 11/1/20 631.35 0.00 13.23 618.12 1,249.40 35 12/1/20 631.35 0.00 8.85 622.50 626.90 36 1/1/21 631.34 0.00 4.44 626.90 0.00Explanation / Answer
Calculation of EMIs at various interest rates
EMI = (P* i * (1+i)n) / ((1+i)n)-1)
EMI when interest rate is 2%
P = 20000
i = 2% pa
= Permonth = 2%/12 = 0.1667%
n = 36 months
EMI = 20000*0.1667%*(1+.0001667)36/ ((1+.0001667)36-1)
EMI = 572.85
So total payment = 572.85*36(installments) = 20622.57
We know that principal payment = 20000
So interest amount = 20622.57-20000
= 622.57
Interest rate 2% 3% 4% 5% 6% 7% 8% 9% 10% Principal amount 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 Permonth Intersrate 0.17 0.25 0.33 0.42 0.50 0.58% 0.67% 0.75% 0.83% n 36.00 36.00 36.00 36.00 36.00 36.00 36.00 36.00 36.00 p*i 33.33 50.00 66.67 83.33 100.00 116.67 133.33 150.00 166.67 (1+i)^36 1.06 1.09 1.13 1.16 1.20 1.23 1.27 1.31 1.35 ((1+i)^36)-1 0.06 0.09 0.13 0.16 0.20 0.23 0.27 0.31 0.35 EMI 572.85 581.62 590.48 599.42 608.44 617.54 626.73 635.99 645.34 Total Paid 20,622.66 20,938.47 21,257.27 21,579.05 21,903.79 22,231.51 22,562.18 22,895.81 23,232.37 Principal Payment 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 20,000.00 Total Interest 622.66 938.47 1,257.27 1,579.05 1,903.79 2,231.51 2,562.18 2,895.81 3,232.37