TI-BASIC:Sigmaprn - Revision history

Maintenance script: Automated superscript correction

2016-02-24T22:24:16Z

Automated superscript correction

← Older revision		Revision as of 22:24, 24 February 2016
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	Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the [[TI-BASIC:Tvm\|tvm_Pmt]] command, we get a value of about -$733.76 for PMT.		Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the [[TI-BASIC:Tvm\|tvm_Pmt]] command, we get a value of about -$733.76 for PMT.

	We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1^^st^^ payment and the 5*12=60^^th^^ payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)		We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1<sup>st</sup> payment and the 5*12=60<sup>th</sup> payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

	= Formulas =		= Formulas =

KermMartian at 19:20, 24 February 2016

2016-02-24T19:20:36Z

← Older revision		Revision as of 19:20, 24 February 2016
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	The formula that the calculator uses for ΣPrn( is in terms of [[TI-BASIC:Bal\|Bal(]]:		The formula that the calculator uses for ΣPrn( is in terms of [[TI-BASIC:Bal\|Bal(]]:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\operatorname{\Sigma Prn}(n_1,n_2)=\operatorname{bal}(n_2)-\operatorname{bal}(n_1)		\operatorname{\Sigma Prn}(n_1,n_2)=\operatorname{bal}(n_2)-\operatorname{bal}(n_1)
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	When the ''roundvalue'' argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:		When the ''roundvalue'' argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\operatorname{\Sigma Prn}(n_1,n_2)=\left(\operatorname{PV}-\frac{\operatorname{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right]		\operatorname{\Sigma Prn}(n_1,n_2)=\left(\operatorname{PV}-\frac{\operatorname{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right]
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	= Error Conditions =		= Error Conditions =
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	* [[TI-BASIC:Bal\|Bal(]]		* [[TI-BASIC:Bal\|Bal(]]
	* [[TI-BASIC:Sigmaint\|ΣInt(]]		* [[TI-BASIC:Sigmaint\|ΣInt(]]
	* [[TI-BASIC:Tvm\|tvm_Pmt]][[Category:TI-BASIC]]		* [[TI-BASIC:Tvm\|tvm_Pmt]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:22:26Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=SIGMAPRN.GIF
|summary=For an [wikipedia:Amortization_schedule amortization schedule], calculates the principal amount paid over a range of payments.
|syntax=ΣPrn(''paymentt1'', ''payment2'', [''roundvalue''])
|location=On the TI-83, press:
# 2nd FINANCE to access the finance menu.
# 0 to select ΣPrn(, or use arrows and ENTER.

On the TI-83+ or higher, press:
# APPS to access the applications menu.
# 1 or ENTER to select Finance...
# 0 to select ΣPrn(, or use arrows and ENTER.
|compatibility=TI-83/84/+/SE
|size=2 bytes
}}

The ΣPrn( command calculates, for an [wikipedia:Amortization_schedule amortization schedule], the principal amount over a range of payments: the portion of those payments that went toward paying off the principal. Its two required arguments are ''payment1'' and ''payment2'', which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

The optional argument, ''roundvalue'', is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using [[TI-BASIC:Round|Round(]] to round the result of ΣPrn( to the same number of digits.

Usually, you will know the values of '''N''', PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣPrn(; virtually always, FV will equal 0.

= Sample Problem =

''Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the principal amount was paid in the first five years?''

We know the values of '''N''', I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). '''N''' is 30*12, and I% is 8/12. PV is just 100000.

Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the [[TI-BASIC:Tvm|tvm_Pmt]] command, we get a value of about -$733.76 for PMT.

We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1^^st^^ payment and the 5*12=60^^th^^ payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

= Formulas =

The formula that the calculator uses for ΣPrn( is in terms of [[TI-BASIC:Bal|Bal(]]:

[[TI-BASIC:Math|Math]]
\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
\operatorname{\Sigma Prn}(n_1,n_2)=\operatorname{bal}(n_2)-\operatorname{bal}(n_1)
[[TI-BASIC:/math|/math]]

When the ''roundvalue'' argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:

[[TI-BASIC:Math|Math]]
\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
\operatorname{\Sigma Prn}(n_1,n_2)=\left(\operatorname{PV}-\frac{\operatorname{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right]
[[TI-BASIC:/math|/math]]

= Error Conditions =

* '''[[TI-BASIC:Errors#domain|ERR:DOMAIN]]''' is thrown if either payment number is negative or a decimal.

= Related Commands =

* [[TI-BASIC:Bal|Bal(]]
* [[TI-BASIC:Sigmaint|ΣInt(]]
* [[TI-BASIC:Tvm|tvm_Pmt]][[Category:TI-BASIC]]
[[Category:TIBD]]