An amount of money is invested in a savings account for two years. It increased by Tk. 102.50 in two years after annual compounding at the rate of 5% per year. What is the amount invested initially?

Question: An amount of money is invested in a savings account for two years. It increased by Tk. 102.50 in two years after annual compounding at the rate of 5% per year. What is the amount invested initially?

Solution:
ধরি, আসল = P টাকা
সময়, n = 2 বছর
মুনাফার হার, r = 5% = 5/100 = 1/20
চক্রবৃদ্ধি মুনাফা = 102.50 টাকা

আমরা জানি, চক্রবৃদ্ধি মুনাফা = P(1 + r)ⁿ - P
⇒ P(1 + 1/20)² - P = 102.50
⇒ P(21/20)² - P = 102.50
⇒ P(441/400) - P = 102.50
⇒ (441P - 400P)/400 = 102.50
⇒ 41P/400 = 102.50
⇒ 41P = 102.50 × 400
⇒ 41P = 41000
⇒ P = 41000/41
∴ P = 1000

সুতরাং, শুরুতে বিনিয়োগকৃত আসলের পরিমাণ ছিল 1000 টাকা।