Sharp EL-733 EL-733A Operation Manual - Page 73

DOLLARS AND CENTS -VS- TEN DIGITS (FINAL PAYMENT CALCULATION) As a conclusion to this financial calculations chapter, let's look at a subject that you likely will find extraneous, but that is worth mentioning. Whenever a payment, or any number for that matter, is calculated by the EL-733A, it is computed to an accuracy of 10 digits. However, whenever U.S. money changes hands, it does so to an accuracy of two decimal places (dollars and cents). On a mortgage payment or any payment stream that extends over a long period of time, if your payment has been calculated to 10 digits, it will be likely be a fraction of a cent high or a fraction of a cent low each time. This small error can accumulate to a few dollars by the end of the contract. However, as usual, there is a way around this: Whenever you have just calculated a payment using the [PIO function, key in that payment, rounded to dollars and cents, and then calculate El . By doing this, you accumulate all the fractions-of-a-cent's to a final value which can be incorporated into the last payment: Example: Calculate the payment on a 30 year mortgage of $95'000 at 10.5% APR (monthly compounding). Accumulate all the inaccuracies into the final payment. Solution: (Make sure that BGN is not in the display) 95'000 M 0® 30 intll TXIA fn 142 10.5 12nciFj [414 M. (Make sure BGN is off) M Result: -869.00 That is your payment. It looks like a fairly round number, but if you press MP [U (to display all the decimal places) you will see that at $869.00 per month, there is a little over 1/5 of a cent that is going unpaid (tsk tsk!). To see what this small error accumulates to over the term of the mortgage, use the following keystokes: PrielF1 M 02 869 H-1 M MO Result: -5.86 So over 30 years, a $5.86 error has accumulated. Add this value to the regular monthly payment to come up with the final month's payment. 2nd FICLI [KW Result: - 874.86 And that is the final payment calculation in this manual. 143