50000 rupees were lent for two and a half years at 8% per annum compound interest finds the compound interest at the end of 3 years.
Answer
Verified
Hint: In this question, we will first calculate the amount from the given data of Rs.50000 at 8% compounded annually for the given period of 3years. After this, we will use the formula to calculate the compound interest.Complete step-by-step solution:
In the question, we have:
P = Rs.50000, r = 8% and t = 3 years.
We know that formula to calculate the amount at compound interest is given as:
$A = p{\left( {1 + \dfrac{r}{{100}}} \right)^t}$....................
(1)
Where A = amount obtained after 3 years
P =principal
r=rate of interest
t = Time for which money is lent.
Putting the values in equation1, we get:
$A = 50000{\left( {1 + \dfrac{8}{{100}}} \right)^3} = 50000 \times {(1.08)^3} = 62,985.6$
Therefore the amount after 3 years = $Rs.62985.6$
Now, we will use the formula to calculate the compound interest.
It is given as:
$\text{Compound interest(CI)} = \text{Amount} – \text{Principal}= A – P$
$ \Rightarrow CI = A
– P$.
Putting the values in the above equation, we have:
$CI = Rs.62985.6 – Rs. 500000 = Rs.12985.6.$
Hence, the required compound interest =$ Rs.12985.6$
Note: In this type of question, we should remember the formula to calculate the amount at the given compound interest. One thing to be noted is that if the rate is given in per annum(P.a.) then take time in the year in formula and if the rate is given in per month then take time in months. This is valid for both simple interest and compound interest.
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
- 100
- 80
- 70
- 50
Answer (Detailed Solution Below)
Option 2 : 80
Free
CT : General Awarensess (Mock Test)
10 Questions 10 Marks 9 Mins
Rate% for 1 year when compounded yearly = 8%
Rate% for 1 year when compounded half-yearly = [4 + 4 + (4 × 4)/100]%
⇒ 8.16%
Difference between rate percent = 8.16% - 8% = 0.16%
Difference between interest = 0.16% of 50000 = 80
∴ The required difference is Rs. 80
Alternate Method
Given:
Principal = Rs. 50,000
Rate = 8%
Formula used:
A1 = P(1 + r)t
A2 = P(1 + \(\frac{r}{{2}}\))2t
Calculation:
When interest is yearly
A1 = P(1 + r)t
⇒ 50,000 × (1 + \(\frac{8}{{100}}\))1
⇒ (50,000 × \(\frac{108}{{100}}\))
⇒ Rs. 54,000
Now,
When interest is half-yearly
A2 = P(1 + \(\frac{r}{{2}}\))2t
⇒ 50,000 × (1 + \(\frac{8}{{200}}\))2
⇒ (50,000 × \(\frac{208}{{200}}\) × \(\frac{208}{{200}}\))
⇒ Rs. (5 × 52 × 208)
⇒ Rs. 54,080
Now,
The difference between the interests on compound half-yearly and yearly = Rs. (54,080 – 54,000)
⇒ Rs. 80
∴ The required difference is Rs. 80
Latest Telangana Police Constable Updates
Last updated on Sep 22, 2022
The Telangana State Level Police Recruitment Board (TSLPRB) has released the provisional answer key for the Prelims exam of Telangana Police Constable. The Prelims exam was conducted on 28th August 2022. Candidates can also raise objections if they find any discrepancies in the answer key. Candidates can raise objections from 8:00 AM on 31st August to 5:00 PM on 2nd September 2022 by uploading supporting Documents/Materials in pdf/jpeg format, as attachments. The Telangana State Level Police Recruitment Board will release the final answer key for the exam after considering objections to the provisional Telangana Police Constable Answer Key
Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!