Correct Answer - Option 1 : ₹ 1640
Given:
Principal = ₹ 16000
Rate = 20%
Time = 6 months = 1/2 year
Interest is compounded quarterly
Concept Used:
If interest is compounded quarterly means interest is calculated in every three months that is 4 times in a year.
We can simply convert this problem into a normal compound interest problem by multiplying the time by 4 and dividing the rate by 4
Formula Used:
Amount = Principal[1 + (Rate/100)]Time
Amount = Principal + Interest
Calculation:
New rate = 20%/4 = 5%
New time = 1/2 × 4 = 2 years
Amount = ₹ 16000[1 + 5/100]2
⇒ ₹ 16000[1 + 1/20]2
⇒ ₹ 16000[21/20]2
⇒ ₹ 16000[441/400]
So, Principal + Interest = ₹ 17640
⇒ Interest = ₹ 17640 – ₹ 16000
⇒ Interest = ₹ 1640
∴ The compound interest on ₹ 16000 at the rate of 20% per annum for 6 months if the interest is compounded quarterly is ₹ 1640
