Question

Problem 5.37 (Paying off Credit Cards) Question 20 of 20 Check My Work (3 remaining) eBook Simon recently received a credit card with a 15% nominal interest rate. With the card, he purchased an Apple iPhone 7 for $384.88. The minimum payment on the card is only $10 per month a. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round Intermediate calculations. Round your answer to the nearest whole number. month(s) b. If Simon makes monthly payments of $35, how many months will it be before he pays off the debt? Do not round Intermediate calculations. Round your answer to the nearest whole number. month(s) c. How much more in total payments will Simon make under the $10-a-month plan than under the $35-a-month plan. Do not round Intermediate calculations, Round your answer to the nearest cent. $

Answer 1

a) We are given the following information:

PMT	10.00
r	20.00%
frequency	12(monthly)
PV	$             384.88

We need to solve the following equation to arrive at the required number of months:

1-(1+ -)-пхirequency frequency PV = PMTX frequency

1-(1 + 0,15 )-nx 12 384.88 = 10 x 0.15 12

n = 4.40

So it will take 4.40 years or 4.4 x 12 = 53 months to payoff the entire loan

$ Month Opening Balance PMT Interest Principal repayment Closing Balance 384.88 1 $ 384.88 $ 10.00 $ 4.81 $ 5.19 $ 379.69 2 $ 379.69 $ 10.00 $ 4.75 $ 5.25 $ 374.44 3 $ 374.44 $ 10.00 $ 4.68 $ 5.32 $ 369.12 4 $ 369.12 $ 10.00 $ 4.61 $ 5.39 $ 363.73 5 $ 363.73 $ 10.00 $ 4.55 $ 5.45 $ 358.28 6 $ 358.28 $ 10.00 $ 4.48 $ 5.52 $ 352.76 7 $ 352.76 $ 10.00 $ 4.41 $ 5.59 $ 347.17 8 $ 347.17 $ 10.00 $ 4.34 $ 5.66 $ 341.51 9 $ 341.51 $ 10.00 $ 4.27 $ 5.73 $ 335.77 10 $ 335.77 $ 10.00 $ 4.20 $ 5.80 $ 329.97 11 $ 329.97 $ 10.00 $ 4.12 $ 5.88 $ 324.10 12 $ 324.10 $ 10.00 $ 4.05 $ 5.95 $ 318.15 13 $ 318.15 $ 10.00 $ 3.98 $ 6.02 $ 312.12 14 $ 312.12 $ 10.00 $ 3.90 $ 6.10 $ 306.03 15 $ 306.03 $ 10.00 $ 3.83 $ 6.17 $ 299.85 16 $ 299.85 $ 10.00 $ 3.75 $ 6.25 $ 293.60 17 $ 293.60 $ 10.00 $ 3.67 $ 6.33 $ 287.27 18 $ 287.27 $ 10.00 $ 3.59 $ 6.41 $ 280.86 19 $ 280.86 $ 10.00 $ 3.51 $ 6.49 $ 274.37 201$ 274.37 $ 10.00 $ 3.43 $ 6.57 $ 267.80 21 $ 267.80 $ 10.00 $ 3.35 $ 6.65 $ 261.15 22 $ 261.15 $ 10.00 $ 3.26 $ 6.74 $ 254.41 23 $ 254.41 $ 10.00 $ 3.18$ 6.82 $ 247.59 24 $ 247.59 $ 10.00 $ 3.09 $ 6.91 $ 240.69 25 $ 240.69 $ 10.00 $ 3.01 $ 6.99 $ 233.70 26 $ 233.70 $ 10.00 $ 2.92 $ 7.08 $ 226.62 27 $ 226.62 $ 10.00 $ 2.83 $ 7.17 $ 219.45 28 $ 219.45 $ 10.00 $ 2.74 $ 7.26 $ 212.19 212.19 $ 10.00 $ 2.65 $ 7.35 $ 204.85 30 $ 204.85 $ 10.00 $ 2.56 $ 7.44 $ 197.41 31 $ 197.41 $ 10.00 $ 2.47 $ 7.53 $ 189.87 32 $ 189.87 $ 10.00 $ 2.37 $ 7.63 $ 182.25 33 $ 182.25 $ 10.00 $ 2.28 $ 7.72 $ 174.53 34 $ 174.53 $ 10.00 $ 2.18$ 7.82 $ 166.71 35 $ 166.71 $ 10.00 $ 2.08 $ 7.92 $ 158.79 36 $ 158.79 $ 10.00 $ 1.98 $ 8.02 $ 150.78 37 $ 150.78 $ 10.00 $ 1.88 $ 8.12 $ 142.66 38 $ 142.66 $ 10.00 $ 1.78 $ 8.22 $ 134.44 39 $ 134.44 $ 10.00 $ 1.68 $ 8.32 $ 126.13 40 $ 126.13 $ 10.00 $ 1.58 $ 8.42 $ 117.70 41 $ 117.70 $ 10.00 $ 1.47 $ 8.53 $ 109.17 42 $ 109.17 $ 10.00 $ 1.36 $ 8.64 $ 100.54 43 $ 100.54 $ 10.00 $ 1.26 $ 8.74 $ 91.79 44 $ 91.79 $ 10.00 $ 1.15 $ 8.85$ 82.94 45 $ 82.94 $ 10.00 $ 1.04 $ 8.96 $ 73.98 46 $ 73.98 $ 10.00 $ 0.92 $ 9.08 $ 64.90 47 $ 64.90 $ 10.00 $ 0.81 $ 9.19 $ 55.71 55.71 $ 10.00 $ 0.70 $ 9.30 $ 46.41 49 $ 46.41 $ 10.00 $ 0.58 $ 9.42 $ 36.99 50 $ 36.99 $ 10.00 $ 0.46 $ 9.54 $ 27.45 51 $ 27.45 $ 10.00 $ 0.34 $ 9.66 $ 17.80 52 $ 17.80 $ 10.00 $ 0.22 $ 9.78 $ 8.02 53 $ 8.02 $ 8.12 $ 0.10 $ 8.02 $ -0.00 $ 528.12 $ 143.24 $ 384.88 48 $

b) If the monthly payment is $35 then we can recalculate the number of months using the same formula as above:

384.88 = 35 1- (1 + 0.15)-nx12 - 0.15 12

n = 0.9919

So it will take 0.9919 years or 0.9919 x 12 = 12 months

s Month Opening Balance PMT Interest Principal repayment Closing Balance 384.88 11 $ 384.88 $ 35.00 $ 4.81 $ 30.19 $ 354.69 2 $ 354.69 $ 35.00 $ 4.43 $ 30.57 $ 324.12 3 $ 324.12 $ 35.00 $ 4.05 $ 30.95$ 293.17 4 $ 293.17 $ 35.00 $ 3.66 $ 31.34 $ 261.83 5 $ 261.83 $ 35.00 $ 3.27 $ 31.73 $ 230.11 6 $ 230.11 $ 35.00 $ 2.88 $ 32.13 $ 197.98 7 $ 197.98 $ 35.00 $ 2.47 $ 32.53 $ 165.45 8 $ 165.45 $ 35.00 $ 2.07 $ 32.93 $ 132.52 9 $ 132.52 $ 35.00 $ 1.66 $ 33.35 $ 99.17 10 $ 99.17 $ 35.00 $ 1.24 $ 33.76 $ 65.41 11 $ 65.41 $ 35.00 $ 0.82 $ 34.18 $ 31.23 12 $ 31.23 $ 31.62 $ 0.39 $ 31.23 $ $ 416.64 $31.76 $ 384.88

c) So total payments paid in $10-a- month loan was $528.12 while that in $35-a-month is $416.64 so the difference is 528.12-416.64 = $111.48