Amortization schedule with periodic payments.Moulton Motors is advertising the f
ID: 2732058 • Letter: A
Question
Amortization schedule with periodic payments.Moulton Motors is advertising the following deal on a used Honda Accord: "Monthly payments of $274.27274.27 for the next 3636 months and this beauty can be yours!" The sticker price of the car is $8 comma 5008,500. If you bought the car, what interest rate would you be paying in both APR and EAR terms? What is the amortization schedule of the first six payments?
If you bought the car, what monthly interest rate would you be paying?
nothing%
(Round to five decimal places.)
If you bought the car, what annual percentage rate (APR) would you be paying?
nothing%
(Round to two decimal places.)
If you bought the car, what effective annual rate (EAR) would you be paying?
nothing%
(Round to two decimal places.)
Prepare the amortization schedule for the first six payments of this car loan. What is the interest expense of the loan in month 1?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 1?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 1?
$nothing
(Round to the nearest cent.)
What is the interest expense of the loan in the month 2?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 2?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 2?
$nothing
(Round to the nearest cent.)
What is the interest expense of the loan in the month 3?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 3?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 3?
$nothing
(Round to the nearest cent.)
What is the interest expense of the loan in the month 4?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 4?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 4?
$nothing
(Round to the nearest cent.)
What is the interest expense of the loan in the month 5?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 5?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 5?
$nothing
(Round to the nearest cent.)
What is the interest expense of the loan in the month 6?
$nothing
(Round to the nearest cent.)
What is the principal reduction of the loan in month 6?
$nothing
(Round to the nearest cent.)
What is the remaining principal of the loan in month 6? Note that following this procedure you can complete the amortization schedule for the entire
3636
payments of the car loan.
$nothing
(Round to the nearest cent.)
Explanation / Answer
Answer: The periodic or monthly interest rate, r, is the solution to the equation :
PV = Payment x (1 – 1/(1+r)n) / r
$8,500 = $274.27 x (1 – 1/(1+r)36) / r
And iterate until you Fnd the monthly rate of 0.835%
Annual Percentage Rate = 0.00835 x 12 = 0.1002 or 10.02%
EAR = 1.0083512– 1 = 10.49%
Amortization Schedule (Can be done effectively on a spread sheet)
Cell A1 is Beginning Balance for month 1
Cell B1 is the Monthly Payment
Cell C1 is the Monthly Interest Expense and is the periodic or monthly interest rate times the beginning balance: A1 * 0.1002/12 (formula for the cell)
Cell D1 is the amount of the monthly payment that is applied to the principal and is the payment minus the interest expense: B1 – C1 (formula for the cell)
Cell E1 is the ending balance after the applying of the monthly payment to interest and principal. It is the beginning balance minus the principal reduction: A1 – D1(formula for the cell).
Cell A2 is the ending balance from the previous month or the value in Cell E1.
Then for cells B2 through E2 copy the formulas down from the row above.
Repeat this for 36 months…
the interest expense of the loan in month 1=70.98
the principal reduction of the loan in month 1=203.30
the remaining principal of the loan in month 1=$8296.71
the interest expense of the loan in the month 2=$69.28
And so on............
Months A B C D E 1 8500.00 274.27 70.98 203.30 8296.71 2 8296.71 274.27 69.28 204.99 8091.71 3 8091.71 274.27 67.57 206.70 7885.01 4 7885.01 274.27 65.84 208.43 7676.58 5 7676.58 274.27 64.10 210.17 7466.41 6 7466.41 274.27 62.34 211.93 7254.48 7 7254.48 274.27 60.57 213.70 7040.79 8 7040.79 274.27 58.79 215.48 6825.31 9 6825.31 274.27 56.99 217.28 6608.03 10 6608.03 274.27 55.18 219.09 6388.94 11 6388.94 274.27 53.35 220.92 6168.01 12 6168.01 274.27 51.50 222.77 5945.25 13 5945.25 274.27 49.64 224.63 5720.62 14 5720.62 274.27 47.77 226.50 5494.12 15 5494.12 274.27 45.88 228.39 5265.72 16 5265.72 274.27 43.97 230.30 5035.42 17 5035.42 274.27 42.05 232.22 4803.20 18 4803.20 274.27 40.11 234.16 4569.03 19 4569.03 274.27 38.15 236.12 4332.91 20 4332.91 274.27 36.18 238.09 4094.82 21 4094.82 274.27 34.19 240.08 3854.75 22 3854.75 274.27 32.19 242.08 3612.66 23 3612.66 274.27 30.17 244.10 3368.56 24 3368.56 274.27 28.13 246.14 3122.42 25 3122.42 274.27 26.07 248.20 2874.22 26 2874.22 274.27 24.00 250.27 2623.95 27 2623.95 274.27 21.91 252.36 2371.59 28 2371.59 274.27 19.80 254.47 2117.12 29 2117.12 274.27 17.68 256.59 1860.53 30 1860.53 274.27 15.54 258.73 1601.79 31 1601.79 274.27 13.37 260.90 1340.90 32 1340.90 274.27 11.20 263.07 1077.83 33 1077.83 274.27 9.00 265.27 812.56 34 812.56 274.27 6.78 267.49 545.07 35 545.07 274.27 4.55 269.72 275.35Related Questions
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