The sum of Rs. 3200 invested at 10% per annum compounded quarterly amounts to Rs. 3362, then find the time period.
- ½ year
- ¼ year
- ¾ year
- 1 year
Answer (Detailed Solution Below)
Option 1 : ½ year
Free
RRB Group D: Memory Based Question Full Test based on 17 Aug 2022
100 Questions 100 Marks 90 Mins
Given:
Principal = Rs 3200
Rate of interest = 10% per annum
Amount = Rs 3362
Concept used:
Amount = P × [1 + (r/100)]t
But here, the amount is calculated quarterly. Then the amount obtained will be:
Amount = P × [1 + r/(n × 100)]nt
Where n is the number of terms, here n = 4.
Calculation:
3362 = 3200 × [1 + 10/(4 × 100]4t
⇒ 3362/3200 = (41/40)4t
⇒ 1681/1600 = (41/40)4t
⇒ (41/40)2 = (41/40)4t
On comparing powers,
⇒ 2 = 4t
⇒ t = 1/2
∴ The time period is 1/2 year.
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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!
What will be the difference between the compound interest (interest is compounded annually) and simple interest on a sum of Rs. 3200 at the rate of 20% per annum for 2 years?
- Rs. 128
- Rs. 148
- Rs. 132
- Rs. 96
Answer (Detailed Solution Below)
Option 1 : Rs. 128
Free
10 Questions 10 Marks 7 Mins
Given:
Principal = Rs. 3200
Rate of interest = 20%
Time = 2 years
Formula Used:
Simple interest = (principal × time × rate) / 100
Successive increase = {a + b + (a × b) / 100}
Calculation:
Simple Interest = (3200 × 20 × 2) / 100
⇒ Simple interest = Rs. 1280
Now,
Compound interest
Rate% = 20%
Time = 2
So {20 + 20 + (20× 20) / 100}
⇒ 44%
⇒Compound interest = 44% of 3200
⇒ Rs. 1408
∴ Difference between compound interest and simple interest = 1408 – 1280 = Rs. 128
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Let's discuss the concepts related to Interest and Simple and Compound Both. Explore more from Quantitative Aptitude here. Learn now!