Rs. 17000 is lent at compound interest at an annual rate of 22 percent for 1 year (compounding annually). If the compounding of interest is done half yearly, then how much more interest will be obtained?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs. 205.7.
We know that,
A = P(1 + r/(n ×100))nt
here, A = Amount,
P = Principal = Rs. 17000,
r = rate = 22% = 0.22,
n = Number of times interest is compounded per year and
t = time = 1 year
here, n = 1
⇒ A = 17000(1 + 0.22/1)1
⇒ A = 17000 × 1.22
⇒ A = Rs. 20740
So,
Interest = Amount - Principal
⇒ Interest = 20740 - 17000
⇒ Interest = Rs. 3740
Now,
When compound half-yearly
here, n = 2
⇒ A = 17000(1 + 0.22/2)2
⇒ A = 17000 × (1 + 0.11)2
⇒ A = 17000 × (1.11)2
⇒ A = 17000 × 1.2321
⇒ A = Rs. 20945.7
⇒ Interest = 20945.7 - 17000
⇒ Interest = Rs. 3945.7
Hence,
Additional interest = 3945.7 - 3740 = Rs. 205.7