economics Aerotron Electronics has just bought a used delivery truck for 15,000.

Question

economics Aerotron Electronics has just bought a used delivery truck for 15,000. The small business paid 1,000 down and financed the rest, with the agreement to pay nothing for the entire first year and then to pay 566.83 at the end of each month over years 2, 3, and 4 (first payment is in 13th month). What nominal interest rate is Aerotron paying on the loan? % What effective interest rate are they paying? % Round your answer to 4 decimal places for a and b. The tolerance is +/- 0.0005. How much of the 14th month's payment is interest? How much is principal? payment interest = and principal = How much of the 18th month's payment is interest? How much is principal? payment interest = and principal = How much of the 22nd month's payment is interest? How much is principal? payment interest = and principal = Round your answers to the nearest whole dollar for c-e. The tolerance is +/- 5.

Explanation / Answer

Loan Amount = 15000 – 1000 = $14000

Monthly Installment (P) = $566.83

Payment is done in each month of year 2, 3 and 4. Thus, a total month of payment is 36.

Let, Monthly interest rate = R

Then

Loan Amount = (P*(1-1/(1+R)^36)/R))/(1+R)^12

Loan Amount = (566.83*(1-1/(1+R)^36)/R)/(1+R)^12

At R = 1.2%

PV of loan payment = $14291.539

At R = 1.3%

PV of loan payment = $13885.76

Thus, as per the method of interpolation,

R = 1.2% + ((PV at 1.2% - Loan amount) / (PV at 1.2% - PV at 1.3%))*(1.3% - 1.2%)

R = 1.2% +((14291.539 – 14000)/( 14291.539 - 13885.76))*(1.3% - 1.2%)

R = 0.012718 = 1.2718% approx

a.

Nominal Interest Rate = 12*R = 12*1.2718% = 15.2616%

b.

Effective Interest Rate = (1+R)^12 – 1 = (1+0.012718)^12 – 1

Effective Interest Rate = 0.163757 = 16.3757%

c.

in 14th month

interest payment = $202.6356

Principal payment = $364.1943

d.

in 18th month

interest payment = $183.7518

Principal payment = $383.0781

Loan Amount = 14000 R = 0.01272 Month Installment Principal Amount Interest Amount Loan Amount Left 1 2 3 4 5 6 7 8 9 10 11 12 16292.59964 13 566.83 359.6207177 207.2092823 15932.97893 14 566.83 364.194374 202.635626 15568.78455 15 566.83 368.8261981 198.0038019 15199.95835 16 566.83 373.5169296 193.3130704 14826.44143 17 566.83 378.267318 188.562682 14448.17411 18 566.83 383.0781217 183.7518783 14065.09599 19 566.83 387.9501093 178.8798907 13677.14588 20 566.83 392.8840587 173.9459413 13284.26182 21 566.83 397.8807582 168.9492418 12886.38106 22 566.83 402.9410057 163.8889943 12483.44005 23 566.83 408.0656094 158.7643906 12075.37444 24 566.83 413.2553878 153.5746122 11662.11906 25 566.83 418.5111698 148.3188302 11243.60789 26 566.83 423.8337949 142.9962051 10819.77409 27 566.83 429.2241131 137.6058869 10390.54998 28 566.83 434.6829854 132.1470146 9955.866993 29 566.83 440.2112836 126.6187164 9515.65571 30 566.83 445.8098907 121.0201093 9069.845819 31 566.83 451.4797009 115.3502991 8618.366118 32 566.83 457.2216197 109.6083803 8161.144499 33 566.83 463.0365643 103.7934357 7698.107934 34 566.83 468.9254633 97.90453671 7229.182471 35 566.83 474.8892573 91.94074267 6754.293214 36 566.83 480.9288989 85.90110109 6273.364315 37 566.83 487.0453526 79.78464735 5786.318962 38 566.83 493.2395954 73.59040456 5293.079367 39 566.83 499.5126166 67.31738338 4793.56675 40 566.83 505.8654181 60.96458193 4287.701332 41 566.83 512.2990145 54.53098554 3775.402317 42 566.83 518.8144333 48.01556667 3256.587884 43 566.83 525.4127153 41.41728471 2731.175169 44 566.83 532.0949142 34.7350858 2199.080255 45 566.83 538.8620973 27.96790268 1660.218157 46 566.83 545.7153455 21.11465453 1114.502812 47 566.83 552.6557532 14.17424676 561.8470586 48 566.83 559.6844291 7.145570892 2.162629533

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