A sum of Rs. 12,000 amounts to Rs. 20,736 in \(1\frac{1}{2}\) years at a certain rate per annum on compound interest, compounded half yearly. What will be the compound interest (in Rs.) of the same sum in 2 years at the same rate on compound interest. If the interest is compounded annually?
Created: 01 Mar 2026 |
Updated: 06 Mar 2026
Updated: 06 Mar 2026
Explanation:
Given: Sum = Rs. 12,000 Amount = Rs. 20,736 Time = 1(1/2) years Compounded half yearly Formula Used: CI = A – P A = P(1 + R/100)n Where CI is compound interest A is amount P is sum/principle R is rate n is number of years Calculation: Time = 1(1/2 years) ⇒ Time = 3/2 years Compounded half-yearly, i.e. Twice a year ⇒ Time = 3/2 × 2 ⇒ Time = 3 Now by using formula, A = P(1 + R/100)n ⇒ 20,736 = 12,000(1 + R/100)3 ⇒ 20,736/12,000 = (1 + R/100)3 ⇒ 216/125 = (1 + R/100)3 Taking cube root on both sides, we get ⇒ 6/5 = 1 + R/100 ⇒ 6/5 – 1 = R/100 ⇒ 1/5 = R/100 ⇒ R = 20% Compounded half yearly Rate was compounded twice a year. ⇒ Rate when compounded yearly = 20 × 2 ⇒ Rate = 40% ⇒ Time = 2 years Compound interest when compounded yearly, A = P(1 + R/100)n ⇒ A = 12,000 (1 + 40/100)2 ⇒ A = 12,000 (1 + 4/10)2 ⇒ A = 12,000 (14/10)2 ⇒ A = 12,000 × 14/10 × 14/10 ⇒ A = 23,520 Now for compound interest, ⇒ CI = 23,520 – 12,000 ⇒ CI = 11,520 ∴ Compound interest, when compounded annually, is Rs. 11,520.
বাংলা সাহিত্য ও ব্যাকরণ হলো বাংলা ভাষার দুটি অবিচ্ছেদ্য অঙ্গ। বাংলা সাহিত্য হলো বাংলা ভাষায় রচিত কবিতা, উপন্যাস, নাটক, গল্পসহ সৃজনশীল ও মননশীল রচনার সমষ্টি, যার সূচনা দশম শতাব্দীতে 'চর্যাপদ' এর মাধ্যমে। অন্যদিকে, বাংলা ব্যাকরণ হলো এমন একটি শাস্ত্র বা বিজ্ঞান, যা বাংলা ভাষার গঠন, প্রকৃতি, ধ্বনি, শব্দ ও বাক্যের নিয়ম-কানুন বিশ্লেষণ করে ভাষার শুদ্ধ রূপ ও প্রয়োগ শেখায়।
💬 Comments (0)