Question

After graduation you decide to buy your first car. You decide you want to get a Toyota because it has a 5 year/50,000 mile warranty. You buy a 2019 Toyota Camry for $35,000 and finance the vehicle through a Bank. Today’s new car loans are 4.29% APR. a. (2 points) If you finance this car for 66 months, what is your monthly payment? b Create an amortization table showing monthly payment, monthly interest and monthly principle paid. After the first year (12 months), how much interest have you paid?

Answer 1

Answer:

(a) Monthly payment of loan=$596.27 Details as follows

A B C D 1 Constant Payment Mortgage or Equated Monthly Installments (EMI) 66 3 EMI is calculated using the formula EMI=[P*r*(1+r)^n]/((1+r)^n)-1 4 Where P= Principal (loan amount), 5 n= Number of installments. 6 r= Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) 7 All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 35000 10 Rate of interest (% p.a)=R= 4.29 No. of months (n)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per month in decimals (r = R/(100*12) D10/(100*12) 0.003575 15 No. of months (n)= N*12 G9*12 66 (1+r)= 1+G14 1.003575 (1+r)^n= G16^G10 1.265578389 [(1+r)^n)-1= G17-1 0.265578389 P*r*(1+r)^n= D9*G14*G17 158.3554959 20 Equated Monthly Insallments (EMI)= [P*r*(1+r)^n]/[(1+r)^n]-1 G19/G18 596.2664986 21 Rounded to $596.27 22

(b) Amortization schedule as follows:

I J K L M N O P Q (6) Shedule of amortization Month Beginning Monthly EMI Interest Principal End Interest balance interest component Component balance Paid till rate =Col (2)*(3) =Col (4)-(5) =Col (2)-(6) date (1) (2) (3) (4) (5) (7) 35000 0.003575 596.27 125.125 471.14 34528.86 2 34528.86 0.003575 596.27 123.4406691 472.83 34056.03 3 34056.03 0.003575 596.27 121.7503168 474.52 33581.52 4 33581.52 0.003575 596.27 120.0539215 476.21 33105.30 33105.30 0.003575 596.27 118.3514615 477.92 32627.39 6 32627.39 0.003575 596.27 116.6429152 479.62 32147.77 7 32147.77 0.003575 596.27 114.9282609 481.34 31666.43 8 31666.43 0.003575 596.27 113.2074767 483.06 31183.37 9 31183.37 0.003575 596.27 111.4805407 484.79 30698.58 1030698.58 0.003575 596.27 109.7474309 486.52 30212.06 11 30212.06 0.003575 596.27 108.0081253 488.26 29723.80 12 29723.80 0.003575 596.27 106.2626016 490.00 29233.80 1388.999 13 29233.80 0.003575 596.27 104.5108376 491.76 28742.05 14 28742.05 0.003575 596.27 102.7528111 493.51 28248.53 15 28248.53 0.003575 596.27 100.9884997 495.28 27753.25

H I J K 16 27753.25 0.003575 17 27256.20 0.003575 18 26757.38 0.003575 19 26256.77 0.003575 20 25754.37 0.003575 21 25250.18 0.003575 22 24744.18 0.003575 23 24236.37 0.003575 24 23726.75 0.003575 25 23215.31 0.003575 26 22702.04 0.003575 27 22186.93 0.003575 28 21669.98 0.003575 29 21151.19 0.003575 30 20630.54 0.003575 31 20108.02 0.003575 3219583.64 0.003575 33 19057.39 0.003575 34 18529.25 0.003575 35 17999.23 0.003575 36 17467.31 0.003575 37 16933.49 0.003575 38 16397.76 0.003575 39 15860.11 0.003575 L M 596.27 99.21788087 596.27 97.44093206 596.27 95.65763066 596.27 93.86795396 596.27 92.07187916 596.27 90.2693834 596.27 88.46044371 596.27 86.64503706 596.27 84.82314034 596.27 82.99473033 596.27 81.15978376 596.27 79.31827726 596.27 77.47018737 596.27 75.61549055 596.27 73.7541632 596.27 71.8861816 596.27 70.01152197 596.27 68.13016043 596.27 66.24207302 596.27 64.3472357 596.27 62.44562433 596.27 60.5372147 596.27 58.62198251 596.27 56.69990337 N 497.05 498.83 500.61 502.40 504.19 506.00 507.81 509.62 511.44 513.27 515.11 516.95 518.80 520.65 522.51 524.38 526.25 528.14 530.02 531.92 533.82 535.73 537.64 539.57 27256.20 26757.38 26256.77 25754.37 25250.18 24744.18 24236.37 23726.75 23215.31 22702.04 22186.93 21669.98 21151.19 20630.54 20108.02 19583.64 19057.39 18529.25 17999.23 17467.31 16933.49 16397.76 15860.11 15320.55

Днік 40 15320.55 0.003575 41 14779.05 0.003575 42 14235.62 0.003575 43 13690.25 0.003575 44 13142.92 0.003575 45 12593.64 0.003575 46 12042.40 0.003575 47 11489.18 0.003575 48 10933.99 0.003575 49 10376.81 0.003575 9817.64 0.003575 9256.47 0.003575 52 8693.30 0.003575 8128.11 0.003575 54 7560.90 0.003575 6991.67 0.003575 56 6420.39 0.003575 5847.08 0.003575 58 5271.72 0.003575 59 4694.30 0.003575 60 4114.81 0.003575 L M. 596.27 54.77095279 596.27 52.83510622 596.27 50.89233899 596.27 48.94262637 596.27 46.98594352 596.27 45.02226554 596.27 43.05156741 596.27 41.07382403 596.27 39.08901022 596.27 37.0971007 596.27 35.0980701 596.27 33.09189297 596.27 31.07854375 596.27 29.05799681 596.27 27.03022642 596.27 24.99520675 596.27 22.95291188 596.27 20.90331581 596.27 18.84639243 596.27 16.78211555 596.27 14.71045888 N 541.50 543.43 545.37 547.32 549.28 551.24 553.21 555.19 557.18 559.17 561.17 563.17 565.19 567.21 569.24 571.27 573.31 575.36 577.42 579.48 581.56 50 14779.05 14235.62 13690.25 13142.92 12593.64 12042.40 11489.18 10933.99 10376.81 9817.64 9256.47 8693.30 8128.11 7560.90 6991.67 6420.39 5847.08 5271.72 4694.30 4114.81 3533.26 57

6991.67 0.003575 6420.39 0.003575 5847.08 0.003575 5271.72 0.003575 4694.30 0.003575 14114.81 0.003575 3533.26 0.003575 2949.62 0.003575 2363.90 0.003575 1776.09 0.003575 1186.17 0.003575 1594.14 0.003575 596.27 24.99520675 596.27 22.95291188 596.27 20.90331581 596.27 18.84639243 596.27 16.78211555 596.27 14.71045888 596.27 12.63139604 596.27 10. 5490055 596.27 8.450945832 596.27 6.349505231 596.27 4.24055198 596.27 2.124059221 571.27 573.31 575.36 57.42 579.48 581.56 583.64 585.72 587.82 589.92 592.03 594.14 6420.39 5847.08 5271.72 4694.30 4114.81 3533.26 2949.62 2363.90 1776.09 1186.17 594.14 0.00 65 66

Total interest paid after 12 months is $1389  as shown in the colored raw of amortization schedule above (sum of interest component during the first 12 months).