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Checking Results

You should not automatically accept the results of any financial calculator without first cross-checking to see that they are reasonable.

Scale and Rounding

For example, you may receive unexpected results when the number of decimal places is not appropriate for the problem.

The table below shows the monthly payment and ending balance for a $200,000 loan with interest rates ranging from 0% to 80%.  There are 360 monthly payments (30 years) with interest compounded monthly.   The loan was amortized with three different calculators each set to 4 decimal places.  We expect the  final balance to be very near 0. 

Rate Payment Balance At End of Period 360
TVM TI BA-II HP 10B
0 -555.5556 -0.0160 -0.0160 -0.0160
1 -643.2790 0.0161 0.0161 0.0161
2 -739.2389 0.0222 0.0224 0.0222
3 -843.2081 -0.0194 -0.0194 -0.0194
4 -954.8306 -0.0054 -0.0051 -0.0054
5 -1,073.6432 0.0411 0.0415 -0.0411
6 -1,199.1011 -0.0507 -0.0507 -0.0507
7 -1,330.6050 -0.0093 -0.0093 -0.0093
8 -1,467.5291 0.0658 0.0676 0.0658
9 -1,609.2452 0.0558 0.0558 0.0558
10 -1,755.1431 0.0907 0.0907 0.0907
20 -3,342.0374 -0.6722 -0.6164 -0.6722
30 -5,000.6893 13.4698 13.4698 13.4698
40 -6,666.7165 -70.6202 -65.6075 -70.6202
50 -8,333.3368 -702.6594 -495.3178 -702.6594
60 -10,000.0002 35,725.1096 35,725.1096 35,725.1097
70 -11,666.6667 200,000.0000 200,000.0000 200,000.0000
80 -13,333.3333 200,000.0000 200,000.0000 200,000.0000

As you can see,  there are minor differences in the results of the three calculators throughout the range of rates due to different rounding conventions, but the final balance is under $1.00 through 20%.  However, the ending balance is well over $1.00 at 30%, and at 70% the original $200,000 loan has not been reduced at all!  The amount of the payment that is applied to the outstanding balance is less than $.0001 for the first payments and so the balance is never reduced.  Using additional decimal places will reduce the error.

 

Signed Values

Normally when you amortize a loan, the present value and payment will have opposite signs since the calculators use a cash flow convention. From the customer point of view, a $10,000 loan represents a positive cash inflow since it is money received and payments are negative cash outflows. From the perspective of a bank, the opposite is true. The present value is a negative cash outflow and the payments are positive inflows.

However, when the present value and payments are both positive or both negative, the calculators differ on how interest should be represented. In this example, a customer has deposited $200,000 in a savings account with an 8% interest rate (a negative outflow). The customer continues to make $500 deposits each month (additional negative outflows). The table shows the result of amortizing the first period using three different calculators:

 
Principal Interest Balance
HP 10B -1,833.333 -1,333.333 -201,833.333
TI BA II -1833.333 +1,333.333 -201,833.333
TVM -1833.333 -1,333.333 -201,833.333


 
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