Compound interest ke niyam: dar wahi, hisab badal jata hai
Compound interest ka niyam ek hai — har avadhi ke ant me byaaj mool rakam me jud jata hai, aur agla byaaj usi badhi hui rakam par lagta hai. Par ek baat jo aksar chhoot jati hai: byaaj kis-kis antar par judta hai, use hi compounding frequency kehte hain. Saal me ek baar jude to yearly, chaar baar jude to quarterly, aur har mahine jude to monthly. Bharat me bank FD aur RD par aam taur par timahi hisab hota hai, PPF aur EPF me saalana, aur bachat khate me bhi aajkal timahi aadhar par byaaj milta hai.
Yahi kaaran hai ki ek hi "7.5%" ki dar har jagah barabar nahi hoti. Asli saalana dar (effective annual rate) nikalne ka tareeka hai: (1 + r/n)^n − 1, jaha n saal me byaaj judne ki baar hai. Frequency jitni zyada, asal dar utni thodi zyada. Do yojanaon ki tulna karte waqt keval ghoshit dar na dekhein — ye bhi dekhein ki byaaj kitni baar judta hai aur beech me nikalne par katauti kya hai.
Ek aur vyavharik niyam: compounding ko samay chahiye. Pehle kuch saal badhotari dheemi lagti hai kyunki byaaj chhoti rakam par lagta hai; aakhri saalo me wahi chakr tezi pakadta hai. Is page ka hisab dar ko poori avadhi sthir manta hai — asal jeevan me daren badalti hain, isliye lambe anumaan ko samay-samay par dobara dekhna chahiye.
🧮 Ek aur hisab: ₹75,000 par quarterly banam yearly
₹75,000 ko 7.5% dar par 8 saal rakhte hain. Agar byaaj saal me ek baar jude, to rakam = ₹75,000 × (1.075)^8 = ₹1,33,761. Wahi paisa har teen mahine jude, to ₹75,000 × (1 + 0.075/4)^32 = ₹1,35,902. Fark sirf ₹2,141 ka hai — chhota, lekin bina ek paisa zyada lagaye, keval judne ki baari-baari se. Avadhi 8 ki jagah 20 saal kar dein to yehi chhota fark hazaro se lakh ki taraf badhne lagta hai; compounding ka khel samay se banta hai, jaadu se nahi.