Calculating APR

[Ampleford]

I have a payment plan, and I'd like to calculate the APR for it. I know that there is a RATE function within Excel, but just can't seem to get it to work.

Original cost = £14,611.00
Initial Payment = £13,205.04 (3 x payments of £441.68)
Followed by 33 payments of £441.68

Total repayment of £15,900.48

Interest payable of £1,289.48.

APR = ???

Can you help?

 

[Richard Schollar]

Here's one way - note it assumes that your first payment occurs 1 period after the initial "receipt" of the original cost. This may well be incorrect (ie they may be timed to occur at the same time):

<b>Excel 2002</b><table cellpadding="2.5px" rules="all" style=";background-color: #FFFFFF;border: 1px solid;border-collapse: collapse; border-color: #A6AAB6"><colgroup><col width="25px" style="background-color: #E0E0F0" /><col /><col /><col /><col /><col /></colgroup><thead><tr style=" background-color: #E0E0F0;text-align: center;color: #161120"><th></th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th></tr></thead><tbody><tr ><td style="color: #161120;text-align: center;">4</td><td style=";">Time</td><td style=";">Flow</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">5</td><td style="text-align: right;;">0</td><td style="text-align: right;;">14611</td><td style="text-align: right;;"></td><td style="text-align: right;;">0.520%</td><td style=";">Periodic Rate</td></tr><tr ><td style="color: #161120;text-align: center;">6</td><td style="text-align: right;;">1</td><td style="text-align: right;;">-1325.04</td><td style="text-align: right;;"></td><td style="text-align: right;;">6.24%</td><td style=";">Nominal</td></tr><tr ><td style="color: #161120;text-align: center;">7</td><td style="text-align: right;;">2</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;">6.42%</td><td style=";">APR</td></tr><tr ><td style="color: #161120;text-align: center;">8</td><td style="text-align: right;;">3</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">9</td><td style="text-align: right;;">4</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">10</td><td style="text-align: right;;">5</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">11</td><td style="text-align: right;;">6</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">12</td><td style="text-align: right;;">7</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">13</td><td style="text-align: right;;">8</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">14</td><td style="text-align: right;;">9</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">15</td><td style="text-align: right;;">10</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">16</td><td style="text-align: right;;">11</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">17</td><td style="text-align: right;;">12</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">18</td><td style="text-align: right;;">13</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">19</td><td style="text-align: right;;">14</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">20</td><td style="text-align: right;;">15</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">21</td><td style="text-align: right;;">16</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">22</td><td style="text-align: right;;">17</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">23</td><td style="text-align: right;;">18</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">24</td><td style="text-align: right;;">19</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">25</td><td style="text-align: right;;">20</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">26</td><td style="text-align: right;;">21</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">27</td><td style="text-align: right;;">22</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">28</td><td style="text-align: right;;">23</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">29</td><td style="text-align: right;;">24</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">30</td><td style="text-align: right;;">25</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">31</td><td style="text-align: right;;">26</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">32</td><td style="text-align: right;;">27</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">33</td><td style="text-align: right;;">28</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">34</td><td style="text-align: right;;">29</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">35</td><td style="text-align: right;;">30</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">36</td><td style="text-align: right;;">31</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">37</td><td style="text-align: right;;">32</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">38</td><td style="text-align: right;;">33</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">39</td><td style="text-align: right;;">34</td><td style="text-align: right;;">-441.68</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">40</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">-1289.48</td><td style=";">Total Interest</td><td style="text-align: right;;"></td></tr></tbody></table><p style="width:3.6em;font-weight:bold;margin:0;padding:0.2em 0.6em 0.2em 0.5em;border: 1px solid #A6AAB6;border-top:none;text-align: center;background-color: #E0E0F0;color: #161120">Sheet1</p><br /><br /><table width="85%" cellpadding="2.5px" rules="all" style=";border: 2px solid black;border-collapse:collapse;padding: 0.4em;background-color: #FFFFFF" ><tr><td style="padding:6px" ><b>Worksheet Formulas</b><table cellpadding="2.5px" width="100%" rules="all" style="border: 1px solid;text-align:center;background-color: #FFFFFF;border-collapse: collapse; border-color: #A6AAB6"><thead><tr style=" background-color: #E0E0F0;color: #161120"><th width="10px">Cell</th><th style="text-align:left;padding-left:5px;">Formula</th></tr></thead><tbody><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">B6</th><td style="text-align:left">=-441.68*3</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">D5</th><td style="text-align:left">=IRR(<font color="Blue">B5:B39</font>)</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">D6</th><td style="text-align:left">=D5*12</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">D7</th><td style="text-align:left">=EFFECT(<font color="Blue">D5*12,12</font>)</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">C40</th><td style="text-align:left">=SUM(<font color="Blue">B5:B39</font>)</td></tr></tbody></table></td></tr></table><br />

 

[Ampleford]

Hi - got it all to work, except my system (Excel 2003) doesn't seem to understand the "Effect" formula?

 

[Richard Schollar]

You need to enable the Analysis Toolpak add-in via Tools>Add-ins to use EFFECT. The actual inner workings of EFFECT are pretty simple though (so you could omit this) and use the following formula instead:

=(1+D5)^12-1

 

[Ampleford]

Delighted sir... Many thanks