Question : A sum was lent for one year at the rate of 16 percent per annum on compound interest (compounding annually). If the compounding had been done half yearly, then the interest would have increased by Rs. 64. What was the sum lent?
Option 1: Rs. 10000
Option 2: Rs. 6000
Option 3: Rs. 14000
Option 4: Rs. 20000
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: Rs. 10000
Solution : We know, Total Amount = Principal × (1 + $\frac{\text{Rate}}{100})^{\text{Time}}$ Let the lending amount be $x$. ⇒ Interest earned with annually compounding = $x (1 + \frac{16}{100}) - x$ = $x \times\frac{116}{100} - x$ = $\frac{116x}{100}-x$ ⇒ Interest earned with half-yearly compounding = $x (1 + \frac{16}{200})^2- x$ = $x(1+\frac{2}{25})^2-x$ = $x(\frac{27}{25})^2- x$ Given, The difference in interest earned is Rs. 64. ⇒ $[x(\frac{27}{25})^2- x] - [\frac{116x}{100}-x] = 64$ ⇒ $x[\frac{729}{625}-\frac{116}{100}]=64$ ⇒ $x[\frac{729}{625}-\frac{29}{25}]=64$ ⇒ $x(\frac{729-725}{625}) = 64$ ⇒ $x\times\frac{4}{625}=64$ ⇒ $x = \frac{64}{4}\times625= 10000$ Hence, the correct answer is Rs. 10,000.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : The difference between simple interest and compound interest (compounding of interest is done annually) on a certain sum of money for 3 years at the rate of 20 percent per annum is Rs. 192. What is the sum?
Question : The compound interest (compounding annually) on a certain sum for 2 years at the rate of 20 percent per annum is Rs. 2420. What will be the simple interest on the same sum for 3 years at the same rate of interest?
Question : At what rate of compound interest (compounding annually) per annum will a sum of Rs. 250000 becomes Rs. 275625 in 2 years?
Question : Find the sum of money invested by a man in a scheme that offers compound interest(compounding annually) at a 6% rate of interest per annum if compound interest for 2 years is Rs. 618.
Question : Rs. 6000 is lent at the rate of 8% per annum on compound interest (compounded quarterly). What will be the compound interest of 6 months?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile