Contest Results from 8/17/01 Email Newsletter
by
Scott Bilker |
|
QUESTION:
You have an outstanding credit card balance of $5,500 at 15.99% APR
(fixed) and you're making payments of $99.87 per month. With those
payments this loan will be paid off in exactly 100 months. You
decide to save money by transferring this balance to an 9.99% APR
(fixed) and keep making the same monthly payment of $99.87. The good
news is that you can now pay off your loan in only 74 months! How
much money do you save? Is it $2,596, $2,182, or $1,768?
ANSWER: $2,596
Since the payment is kept constant, the total savings is equal
to the number of payments not paid. It takes 100 payments to pay off the
15.99% loan and only 74 payments to pay off the 9.99% loan.
Therefore, you save 26 payments or 26
times $99.87, which is $2,596.62 when comparing the savings over a
100-month period.
It's important to recognize that
you're really saving money THE ENTIRE TIME! The savings is relative
to every point in time. In the problem I implied that you find the
savings over the entire 100 month period, however, there are
savings every month.
Let's compare both loans one month at
a time. Before the first payment, each loan has an unpaid balance of
$5,500. Total savings is zero. However, after the first payment is
made, the balance remaining on the 15.99% loan is $5,473.42 and the
balance for the 9.99% loan is $5,445.92. That means that you saved
the difference, $25.50, after the first payment.
The 9.99% loan is paid off at
payment number 74 which means its balance is zero. So what would
you still owe on the 15.99% loan? That amount is $2,181.97.
From this point forward all the
payments that would have been made to the 15.99% are saved because
you have the 9.99% loan.
|
Month |
15.99%
loan balance |
9.99%
loan balance |
Savings |
|
0 |
$5,500.00 |
$5,500.00 |
$0.00 |
|
1 |
$5,473.42 |
$5,445.92 |
$27.50 |
|
2 |
$5,446.48 |
$5,391.38 |
$55.10 |
|
3 |
$5,419.19 |
$5,336.40 |
$82.79 |
|
4 |
$5,391.53 |
$5,280.95 |
$110.57 |
|
5 |
$5,363.50 |
$5,225.05 |
$138.45 |
|
6 |
$5,335.10 |
$5,168.68 |
$166.42 |
|
7 |
$5,306.32 |
$5,111.84 |
$194.48 |
|
8 |
$5,277.15 |
$5,054.52 |
$222.63 |
|
9 |
$5,247.60 |
$4,996.73 |
$250.87 |
|
10 |
$5,217.66 |
$4,938.46 |
$279.20 |
|
11 |
$5,187.31 |
$4,879.70 |
$307.61 |
|
12 |
$5,156.56 |
$4,820.45 |
$336.11 |
|
13 |
$5,125.40 |
$4,760.71 |
$364.69 |
|
14 |
$5,093.83 |
$4,700.48 |
$393.35 |
|
15 |
$5,061.83 |
$4,639.74 |
$422.10 |
|
16 |
$5,029.41 |
$4,578.49 |
$450.92 |
|
17 |
$4,996.56 |
$4,516.74 |
$479.82 |
|
18 |
$4,963.27 |
$4,454.47 |
$508.80 |
|
19 |
$4,929.53 |
$4,391.69 |
$537.85 |
|
20 |
$4,895.35 |
$4,328.38 |
$566.97 |
|
21 |
$4,860.71 |
$4,264.54 |
$596.17 |
|
22 |
$4,825.61 |
$4,200.17 |
$625.44 |
|
23 |
$4,790.04 |
$4,135.27 |
$654.77 |
|
24 |
$4,754.00 |
$4,069.83 |
$684.17 |
|
25 |
$4,717.48 |
$4,003.84 |
$713.64 |
|
26 |
$4,680.47 |
$3,937.30 |
$743.17 |
|
27 |
$4,642.96 |
$3,870.21 |
$772.76 |
|
28 |
$4,604.96 |
$3,802.56 |
$802.41 |
|
29 |
$4,566.45 |
$3,734.34 |
$832.11 |
|
30 |
$4,527.43 |
$3,665.56 |
$861.87 |
|
31 |
$4,487.89 |
$3,596.21 |
$891.68 |
|
32 |
$4,447.82 |
$3,526.27 |
$921.54 |
|
33 |
$4,407.22 |
$3,455.76 |
$951.46 |
|
34 |
$4,366.07 |
$3,384.66 |
$981.41 |
|
35 |
$4,324.38 |
$3,312.97 |
$1,011.41 |
|
36 |
$4,282.13 |
$3,240.68 |
$1,041.45 |
|
37 |
$4,239.32 |
$3,167.79 |
$1,071.54 |
|
38 |
$4,195.94 |
$3,094.29 |
$1,101.65 |
|
39 |
$4,151.98 |
$3,020.18 |
$1,131.80 |
|
40 |
$4,107.44 |
$2,945.45 |
$1,161.99 |
|
41 |
$4,062.30 |
$2,870.10 |
$1,192.20 |
|
42 |
$4,016.56 |
$2,794.13 |
$1,222.43 |
|
43 |
$3,970.21 |
$2,717.52 |
$1,252.69 |
|
44 |
$3,923.24 |
$2,640.27 |
$1,282.97 |
|
45 |
$3,875.65 |
$2,562.38 |
$1,313.27 |
|
46 |
$3,827.42 |
$2,483.84 |
$1,343.58 |
|
47 |
$3,778.55 |
$2,404.65 |
$1,373.90 |
|
48 |
$3,729.03 |
$2,324.80 |
$1,404.23 |
|
49 |
$3,678.85 |
$2,244.28 |
$1,434.57 |
|
50 |
$3,628.00 |
$2,163.10 |
$1,464.91 |
|
51 |
$3,576.48 |
$2,081.23 |
$1,495.24 |
|
52 |
$3,524.26 |
$1,998.69 |
$1,525.57 |
|
53 |
$3,471.35 |
$1,915.46 |
$1,555.89 |
|
54 |
$3,417.74 |
$1,831.54 |
$1,586.20 |
|
55 |
$3,363.41 |
$1,746.91 |
$1,616.50 |
|
56 |
$3,308.36 |
$1,661.59 |
$1,646.77 |
|
57 |
$3,252.57 |
$1,575.55 |
$1,677.02 |
|
58 |
$3,196.04 |
$1,488.80 |
$1,707.25 |
|
59 |
$3,138.76 |
$1,401.32 |
$1,737.44 |
|
60 |
$3,080.71 |
$1,313.12 |
$1,767.60 |
|
61 |
$3,021.89 |
$1,224.18 |
$1,797.72 |
|
62 |
$2,962.29 |
$1,134.50 |
$1,827.79 |
|
63 |
$2,901.89 |
$1,044.07 |
$1,857.82 |
|
64 |
$2,840.69 |
$952.90 |
$1,887.80 |
|
65 |
$2,778.67 |
$860.96 |
$1,917.71 |
|
66 |
$2,715.83 |
$768.26 |
$1,947.57 |
|
67 |
$2,652.15 |
$674.78 |
$1,977.37 |
|
68 |
$2,587.62 |
$580.53 |
$2,007.09 |
|
69 |
$2,522.23 |
$485.49 |
$2,036.74 |
|
70 |
$2,455.97 |
$389.66 |
$2,066.30 |
|
71 |
$2,388.82 |
$293.04 |
$2,095.78 |
|
72 |
$2,320.78 |
$195.61 |
$2,125.18 |
|
73 |
$2,251.84 |
$97.37 |
$2,154.47 |
|
74 |
$2,181.97 |
$0.00 |
$2,181.97 |
|
75 |
$2,111.18 |
-$99.87 |
$2,211.05 |
|
76 |
$2,039.44 |
-$199.74 |
$2,239.18 |
|
77 |
$1,966.74 |
-$299.61 |
$2,266.35 |
|
78 |
$1,893.08 |
-$399.48 |
$2,292.56 |
|
79 |
$1,818.44 |
-$499.35 |
$2,317.79 |
|
80 |
$1,742.80 |
-$599.22 |
$2,342.02 |
|
81 |
$1,666.15 |
-$699.09 |
$2,365.24 |
|
82 |
$1,588.48 |
-$798.96 |
$2,387.44 |
|
83 |
$1,509.78 |
-$898.83 |
$2,408.61 |
|
84 |
$1,430.03 |
-$998.70 |
$2,428.73 |
|
85 |
$1,349.21 |
-$1,098.57 |
$2,447.78 |
|
86 |
$1,267.32 |
-$1,198.44 |
$2,465.76 |
|
87 |
$1,184.34 |
-$1,298.31 |
$2,482.65 |
|
88 |
$1,100.25 |
-$1,398.18 |
$2,498.43 |
|
89 |
$1,015.04 |
-$1,498.05 |
$2,513.09 |
|
90 |
$928.69 |
-$1,597.92 |
$2,526.61 |
|
91 |
$841.20 |
-$1,697.79 |
$2,538.99 |
|
92 |
$752.54 |
-$1,797.66 |
$2,550.20 |
|
93 |
$662.70 |
-$1,897.53 |
$2,560.23 |
|
94 |
$571.66 |
-$1,997.40 |
$2,569.06 |
|
95 |
$479.40 |
-$2,097.27 |
$2,576.67 |
|
96 |
$385.92 |
-$2,197.14 |
$2,583.06 |
|
97 |
$291.19 |
-$2,297.01 |
$2,588.20 |
|
98 |
$195.20 |
-$2,396.88 |
$2,592.08 |
|
99 |
$97.93 |
-$2,496.75 |
$2,594.68 |
|
100 |
$0.00 |
-$2,596.62 |
$2,596.62 |
|
101 |
-$99.87 |
-$2,696.49 |
$2,596.62 |
|
102 |
-$199.74 |
-$2,796.36 |
$2,596.62 |
|
103 |
-$299.61 |
-$2,896.23 |
$2,596.62 |
|
104 |
-$399.48 |
-$2,996.10 |
$2,596.62 |
|
105 |
-$499.35 |
-$3,095.97 |
$2,596.62 |
|
106 |
-$599.22 |
-$3,195.84 |
$2,596.62 |
|
107 |
-$699.09 |
-$3,295.71 |
$2,596.62 |
|
108 |
-$798.96 |
-$3,395.58 |
$2,596.62 |
--End--
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