First we need to create ‘catalog_product_prices.xml’ at below location using the given code.

appcodeMagemonkeysDiscountpercentageviewbaselayoutcatalog_product_prices.xml

<?xml version="1.0" encoding="UTF-8"?>
<layout xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/layout_generic.xsd">
    <referenceBlock name="render.product.prices">
        <arguments>
            <argument name="default" xsi:type="array">
                <item name="prices" xsi:type="array">
                <item name="final_price" xsi:type="array">
                    <item name="render_class" xsi:type="string">MagentoCatalogPricingRenderFinalPriceBox</item>
                    <item name="render_template" xsi:type="string">Magemonkeys_Discountpercentage::product/price/final_price.phtml</item>
                </item>
                </item>
            </argument>
        </arguments>
    </referenceBlock>
</layout>

And create one more file to display the price and discount percentage on the product detail page.

appcodeMagemonkeysDiscountpercentageviewbasetemplatesproductpricefinal_price.phtml

<?php
$priceModel = $block->getPriceType('regular_price');
$finalPriceModel = $block->getPriceType('final_price');
$idSuffix = $block->getIdSuffix() ? $block->getIdSuffix() : '';
$schema = ($block->getZone() == 'item_view') ? true : false;
?>
<?php if ($block->hasSpecialPrice()): ?>
	<span class="special-price">
        <?php  echo $block->renderAmount($finalPriceModel->getAmount(), [
            'display_label' 	=> __('Special Price'),
            'price_id'      	=> $block->getPriceId('product-price-' . $idSuffix),
    	    'price_type'    	=> 'finalPrice',
            'include_container' => true,
            'schema' => $schema
    	]); ?>
    </span>
	<span>
	<?php
	$item = $block->getSaleableItem();
    $_savePercent = 100 - round(((float)$item->getFinalPrice() / (float)$item->getPrice()) * 100);
	echo '<b style="color:#008000">'.$_savePercent . '% off </b>';
	?>
    </span>
	<span class="old-price">
        <?php  echo $block->renderAmount($priceModel->getAmount(), [
        	'display_label' 	=> __('Regular Price'),
            'price_id'      	=> $block->getPriceId('old-price-' . $idSuffix),
            'price_type'    	=> 'oldPrice',
            'include_container' => true,
            'skip_adjustments'  => true
	    ]); ?>
    </span>
<?php else: ?>
    <?php  echo $block->renderAmount($finalPriceModel->getAmount(), [
        'price_id'      	=> $block->getPriceId('product-price-' . $idSuffix),
        'price_type'    	=> 'finalPrice',
        'include_container' => true,
    	'schema' => $schema
	]); ?>
<?php endif; ?>
 
<?php if ($block->showMinimalPrice()): ?>
	<?php if ($block->getUseLinkForAsLowAs()):?>
    	<a href="<?=  $block->getSaleableItem()->getProductUrl() ?>" class="minimal-price-link">
            <?= $block->renderAmountMinimal() ?>
        </a>
	<?php else:?>
    	<span class="minimal-price-link">
            <?=  $block->renderAmountMinimal() ?>
        </span>
	<?php endif?>
<?php endif; ?>

Output :