Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 360784 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0528 1209528 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0528 1209528 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1187 4112344 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1200 4139992 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1207 4157704 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1208 4188736 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1218 4211456 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1218 4211456 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1780 4846536 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1806 4947520 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1812 4968448 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1894 5041240 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1895 5041496 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182 Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360784 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0528 1209528 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0528 1209528 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1187 4112344 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1200 4139992 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1207 4157704 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1208 4188736 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1218 4211456 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1218 4211456 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1780 4846536 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1806 4947520 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1812 4968448 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3108 12603344 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3110 12603744 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3110 12603744 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3112 12611992 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3115 12613728 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3121 12646776 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3121 12647176 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3122 12647256 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Calculating Equal Monthly Repayments

Loans are usually arranged to be repaid at a constant fixed monthly rate. This means that to start with a large fraction of the repayment made each month is used to pay interest. As time progresses the amount used to pay interest decreases and with the last payment the loan is paid off completely.

It is quite tricky to calculate the month repayment. The method is illustrated in this example.

A loan of £500 is taken out at 11% annual interest to be repaid at a fixed monthly rate. Interest is to be charged from the date of the loan and the first repayment is to be made a month after the loan is taken out. Find the monthly repayment.

Call the monthly repayment x. Since the annual rate of interest is 11%, the monthly rate of interest is the solution to

After a month the amount owing in £ isand after the first monthly payment the amount owing is

After two months the amount owing in £ isand after the second monthly payment the amount owing is

After three months the amount owing in £ isand after the second monthly payment the amount owing is

We will carry on in the same way, until after two years, twenty four monthly repayments, the whole loan is paid off. After the last monthly payment there is no money left owing so

The expression on the right is a geometric series with first termand common ratioso the right hand side equalsand

Hence

Substituting the value ofinto this expression gives a monthly repayment of £23.18 to the nearest penny. The total amount repaid is £556.41 to the nearest penny.

Add comment

Security code
Refresh