# APRC v APR Equation



## MichaelRSnow (Apr 15, 2011)

I know this is not exactly an excel based question but i'm sure you cleaver guys can help?

*Can anyone tell me how the new proposed EU wide APRC equation is different to the current <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-comffice:smarttags" /><st1:country-region w:st="on"><st1lace w:st="on">UK</st1lace></st1:country-region> APR in term of APR result/affect on the consumer?<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>*
*<o> </o>*
*Proposed EU APRC <o></o>*
<o> </o>
The basic equation, which establishes the annual percentage rate of charge (APRC), equates, on an annual basis, the total present value of drawdowns on the one hand and the total present value of repayments and payments of charges on the other hand, i.e.:<o></o>
<o> </o>
<TABLE class=MsoNormalTable style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; MARGIN: auto auto auto 4.65pt; BORDER-LEFT: medium none; WIDTH: 243.75pt; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid white .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insidev: .5pt solid white" cellSpacing=0 cellPadding=0 width=325 border=1><TBODY><TR style="HEIGHT: 55.5pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: white 1pt solid; WIDTH: 26.45pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt" width=35>m
∑
k=1<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 25.15pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=34>Ck<o></o>
</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 61.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=83>(1+X) -tk<o></o>
</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 11.8pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=16>=<o></o>
</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 26.45pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" width=35>m'
∑
1=1<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 25.95pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=35>D1<o></o>
</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 66.05pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 55.5pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=88>(1+X) -s1<o></o>
</TD></TR></TBODY></TABLE>
<o> </o>
X is the APRC<o></o>
m is the number of the last drawdown<o></o>
k is the number of a drawdown, thus 1 ≤ k ≤ m<o></o>
Ck is the amount of drawdown k<o></o>
tk is the interval, expressed in years and fractions of a year, between the date of the first drawdown and the date of each subsequent drawdown, thus t1 = 0<o></o>
m' is the number of the last repayment or payment of charges<o></o>
l is the number of a repayment or payment of charges<o></o>
Dl is the amount of a repayment or payment of charges<o></o>
sl is the interval, expressed in years and fractions of a year, between the date of the first drawdown and the date of each repayment or payment of charges.<o></o>
<o> </o>
<o> </o>
*Current <st1:country-region w:st="on"><st1lace w:st="on">UK</st1lace></st1:country-region> APR<o></o>*
*<o> </o>*
For any credit agreement, the annual percentage rate (APR) is the correct value of _i _in the mathematical   equation given below, expressed as a percentage:<o></o>
<o> </o>
<TABLE class=MsoNormalTable style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; MARGIN: auto auto auto 4.65pt; BORDER-LEFT: medium none; WIDTH: 148pt; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid white .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insidev: .5pt solid white" cellSpacing=0 cellPadding=0 width=197 border=1><TBODY><TR style="HEIGHT: 50.25pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: white 1pt solid; WIDTH: 29pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 50.25pt; mso-border-alt: solid white .5pt" width=39>K=m
∑
K=1<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 40pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 50.25pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" width=53>AK
____
(1+i) tk<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 11pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 50.25pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" noWrap width=15>=<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 27pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 50.25pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" width=36>K'=m'
∑
K'=1<o></o>​</TD><TD style="BORDER-RIGHT: white 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: white 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: white; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 41pt; PADDING-TOP: 0cm; BORDER-BOTTOM: white 1pt solid; HEIGHT: 50.25pt; mso-border-alt: solid white .5pt; mso-border-left-alt: solid white .5pt" width=55>A'K'
____
(1+i) tk'<o></o>​</TD></TR></TBODY></TABLE>
<o> </o>
<o> </o>
MEANING OF LETTERS AND SYMBOLS:<o></o>
_K _is the number identifying a particular advance of credit;<o></o>
_K’ _is the number identifying a particular instalment;<o></o>
_AK _is the amount of advance K;<o></o>
_A’K’ _is the amount of instalment K’;<o></o>
Σ represents the sum of all the terms indicated;<o></o>
_m _is the number of advances of credit;<o></o>
_m’ _is the total number of instalments;<o></o>
_tK _is the interval, expressed in years, between the relevant date and the<o></o>
date of advance K;<o></o>
_tK’ _is the interval, expressed in years, between the relevant date and the<o></o>
date of instalment K’;<o></o>
_i _is the APR, expressed as a decimal.<o></o>


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## JackDanIce (Apr 15, 2011)

n/a


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## WaterGypsy (Apr 15, 2011)

It's Friday for pity's sake ..... not that I think I could give a reasoned answer any other day of the week 

I'd be surprised if anyone really understands it - looks like the workings of a committee to me .... maybe that's why the world has ended up in such a financial mess


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## aronne123 (Oct 18, 2011)

Hi, can anyone check/confirm if the complex equation relating to the proposed EU APRC can be computed on Excel? Thanks.


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## mikerickson (Oct 18, 2011)

The sum of a finite series, yes it can be calculated in Excel.


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