سود مرکب چیست؟
ر صورتی که سرمایه گذاری در بازارهای مختلف را تجربه کرده باشید با مفهوم سود و بازدهی آشنا هستید. همچنین میدانید که هر بازاری قانون خاصی برای کسب بازدهی دارد. اگر سرمایه خود را در بانک سپرده گذاری کرده باشید، متوجه شدید که سالانه مقدار مشخصی بر روی سرمایه اولیه شما اضافه میشود.
![](https://academychartkhani.ir/wp-content/uploads/2021/11/compound-interest-780x455-1.png)
اگر سود کسب شده را از حساب خود خارج کنید، همچنان بر روی اصل پول خود سود دریافت میکنید. همچنین در صورتی که اقدام به خرید طلا یا ارز نمایید، تنها از مابهالتفاوت قیمت خرید با قیمت روز آنها سود خواهید داشت. اما اگر در بازار بورس فعال باشید، سود تنها بر اصل سرمایه شما اضافه نخواهد شد. به این معنی که اگر مبلغی را ابتدا سرمایه گذاری کرده باشید و درصدی سود بر روی آن آمده باشد، در روزهای بعد میزان سود به صورت تصاعدی بیشتر خواهد شد و با میزان درصد سود یکسان، سود کسب شده در یک روز بیشتر از روز دیگر خواهد بود. علت این اتفاق این است که بازدهی در بازار سهام و بورس به صورت سود مرکب محاسبه میشود. مفهوم سود مرکب را در ادامه بیان میکنیم.
انواع سود
همانطور که در مقالات قبل توضیح دادیم سود یا بازدهی پاداشی است که بر روی سرمایه گذاری خود در مدت زمان مشخص به دست میآوریم. به عبارت دیگر بهره، مقدار پولی است که شخص وامگیرنده به عنوان هزینه قرض به شخص وام دهنده پرداخت میکند. بهره همچنین بازدهی برای سرمایه گذاری بر روی دارایی های مالی مختلف است. با توجه به وجود ابزارهای مالی متعدد در بازار سرمایه، انواع بهره نیز وجود دارد. از نظر نوع محاسبه بهره، دو نوع بهره ساده و بهره مرکب در بازار وجود دارد. در صورتی که سود، تنها بازدهی بر روی اصل سرمایه باشد، سود یا بهره ساده به آن میگویند. در روش سود ساده، بهره دریافتی سرمایه گذاری نمیشود و تنها بهرهی دریافتی از همان سرمایه اولیه پرداخت میشود. اما هنگامی که بازدهی بر روی اصل سرمایه به اضافه سودهای گذشته حساب شود، سود یا بهره مرکب است.
سود مرکب یا Compound Interest سود ترکیب شده یا مضاعف است. مرکب شدن بهره به این معنی است که بر روی بهره و اصل پول، بهره دریافت شود. بنابراین سود رشد سریعتر و بیشتری خواهد داشت. در بلند مدت بهره مرکب خود را بیشتر نشان میدهد و بازدهی بر اصل مبلغ و سود نسبت به حالت سود ساده، بسیار بیشتر خواهد شد. به عبارت دیگر سود مرکب اصل سرمایه را به صورت نمایی افزایش میدهد. بهره مرکب را بهره بر سود نیز میتوان دانست.
محاسبه سود ساده و سود مرکب
همانطور گه گفتیم در روش سود ساده یا Simple Interest فرض بر این است که سودهای کسب شده در برهههای زمانی مختلف به سرمایه اضافه نمیشود و بازده سودهای حاصل محاسبه نمیشود. در محاسبه سود به روش ساده تنها از اصل سرمایه استفاده میشود.
![](https://academychartkhani.ir/wp-content/uploads/2021/11/5125977.jpg)
معادله بهره ساده به شکل زیر است:
Simple Interest=P × i × n
P : اصل سرمایه
i : نرخ بهره سالانه
n : مدت زمان
اما برای محاسبه سود مرکب هم اصل سرمایه و هم سود آن در معادله آورده میشود و لازم است میزان مبلغ کل سرمایه در مدت زمان مشخص را از سرمایه اولیه کسر کنیم.
معادله سود مرکب به صورت زیر است:
Compound Interest = [ P (1+i)^n ]-P
Compound Interest = P [ (1+i)^n-1 ]
P : اصل سرمایه
i : درصد نرخ بهره
n : تعداد دوره دریافت سود
با توجه به این معادله هرچه تعداد دوره دریافت سود بیشتر باشد، سود دریافتی نیز بیشتر میشود. بنابراین زمان نقش بسیار کلیدی در سرمایه گذاری با سود مرکب دارد. سرمایه گذاران باید دورههای بلندمدت را برای نگهداری سرمایه خود در نظر بگیرند تا بازدهی بالاتری نسبت به سایر روشها کسب کنند.
این که برای بازدهی از کدام روش استفاده کنید، تفاوت قابل ملاحظهای در بهره دریافتی خواهد داشت. میتوان گفت که سود مرکب سرمایه را بیشتر کرده و سرمایه گذار ثروت بیشتری را کسب خواهد کرد.
مثال
برای درک بهتر موضوع در این قسمت از دو روش محاسبه سود ساده و سود مرکب بازدهی یک سرمایه گذاری را محاسبه میکنیم.
فرض کنید که شخصی ۱ میلیارد تومان را در حساب سپرده بانکی خود سپرده گذاری کرده است. این فرد پول خود را برای سه سال با سود سالانه ۲۰ درصد سرمایه گذاری کرده است. بازدهی کسب شده برای فرد در بازه سه ساله برابر است با:
۱۰۰۰۰۰۰۰۰۰ × ۲۰% × ۳ = سود = ۲۰۰۰۰۰۰۰۰
در سال دوم بازدهی فرد برابر خواهد شد با:
سود =۱،۲۰۰،۰۰۰،۰۰۰ [ (۱+۲۰٪)-۱] =۲۴۰،۰۰۰،۰۰۰
و سال سوم
سود =۱،۴۴۰،۰۰۰،۰۰۰ [ (۱+۲۰٪)-۱]=۲۸۸،۰۰۰،۰۰۰
که در مجموع کل سود فرد در این سه سال برابر خواهد بود با:
مجموع سود = ۲۰۰،۰۰۰،۰۰۰ + ۲۴۰،۰۰۰،۰۰۰+۲۸۸،۰۰۰،۰۰۰ = ۷۲۸،۰۰۰،۰۰۰
یا می توان محاسبه بازدهی را به صورت زیر انجام داد:
سود =۱۰۰۰۰۰۰۰۰۰[ (۱+۲۰٪)^۳-۱ ]= ۷۲۸،۰۰۰،۰۰۰
به این مثال ساده توجه کنید:
تصور کنید دو شخص متفاوت در یک زمان مشخص، مبلغ یکصد میلیون تومان را برای مدت ۱۰ سال در سهام شرکتی با نسبت P/E:5 سرمایه گذاری میکنند؛ شخص اول تصمیم میگیرد سودهای نقدی دریافتی از سهام خود را در یک حساب جاری پسانداز کرده و شخص دوم نیز تصمیم میگیرد از سودهای نقدی دریافتی برای سرمایه گذاری مجدد در سهام شرکت مورد نظر استفاده کرده و از این طریق از سود مرکب بهرهمند شود.
با فرض ثابت ماندن نسبت P/E شرکت و همچنین ثابت ماندن قیمت هر برگ سهم، با توجه به فرمول بالا، بازدهی سرمایه گذاری این دو شخص در پایان سال دهم به شکل زیر باهم متفاوت خواهد بود:
سود سرمایهگذاری شخص اول = ۱۰۰*۲۰%*۱۰ = ۲۰۰ میلیون تومان
سود سرمایهگذاری شخص دوم = ۱۰۰ * ۹^(۱٫۲) = ۵۱۹٫۹۷ میلیون تومان
بدین ترتیب سود سرمایه گذاری شخصی که با دید کسب سود مرکب سرمایهگذاری کرده پس از ۱۰ سال اختلاف چشمگیری با سرمایهگذاران دیگر دارد.
مطالب بیشتر:
مطالب زیر را حتما مطالعه کنید
مدیریت سرمایه چیست؟
مدیریت سرمایه چیست؟
بک تست برای متاتریدر۴
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