9514 1404 393
Answer:
more significant figures than in the answer
interest is reported to 2 decimal places when working with money
Step-by-step explanation:
Sums of money can involve large numbers of significant figures. A billion dollars, accurate to the penny, has 12 significant digits. Everyday finance may not involve billions of dollars, but measures of world economic activity may involve substantially more.
In general, if you want interest rate calculations accurate to the penny, the number of significant digits in the interest rate used must match or exceed the number of significant digits in the end result of the computation.
A million-dollar loan may have payments in the $10,000 range or higher, requiring 7 or 8 significant digits to express the payment value. Hence its computation should be made using interest rates accurate to 7 or 8 significant figures.
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<u>Example</u>:
$1,800,000 loan for 15 years at 3.2% interest. The monthly payment is given by ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . for principal P at rate r for t years
The payment is expected to be in the $10,000 range, so will have 7 significant figures. If we round the monthly interest rate to 7 <em>decimal places</em>, we get ...
A = 1.8×10^6(0.0026667)/(1 -(1.0026667^-180)) = 12,604.38
If we round the monthly interest rate to 8 <em>significant figures</em>, we get ...
A = 1.8×10^6(0.0026666667)/(1 -(1.0026666667^-180)) = 12,604.34
Notice there is a difference in the last digit of the payment value. We should also note here that there was <em>no rounding at any point in the calculation until the final answer</em>.
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Money amounts are generally rounded to the nearest penny <em>when reported on statements of account</em>. That is, interest amounts are rounded, and the account value is maintained to two decimal places. Because of this, payment-by-payment loan amortization schedules may differ from the calculated values arrived at using formulas such as the one above.
For tax purposes, the amount of tax due may be maintained to a number of decimal digits greater than those that appear on the pay stub. A pay-period tax due of 5.3333, for example, may be charged as 5.33 for two pay periods and 5.34 for the third pay period. The idea is to make the yearly total come out right. Usually, 4 or 5 decimal places will be sufficient for this purpose.
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The short answer is ...
enough significant digits to ensure appropriate accuracy of the computed result
(for penny-accurate computations in the trillion-dollar range, 18 significant digits or more may be required.)
interest will be reported to 2 decimal places when working with money
