Find the amount and compound interest on Rs. 20000 for 1 year at 10% per annum compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Answers
Solution :-
Case 1) :-
→ Principal = Rs.20000
→ Rate = 10% compounded half yearly. So, R = (10/2) = 5% per yearly .
→ Time = 1 year. ( since rate is half yearly.) Time will be = 1 * 2 = 2 years.
→ Amount = Principal * [1 + (Rate/100)]^(Time)
Putting all values now, we get,
→ A = 20000[ 1 + (5/100)]²
→ A = 20000[ 1 + (1/20)]²
→ A = 20000[21/20]²
→ A = 20000 * (441/400)
→ A = Rs.22050.
Therefore,
→ CI = Amount - Principal
→ CI = 22050 - 20000
→ CI = Rs.2050.
___________
Case 2 :-
→ Principal = Rs.20000
→ Rate = 10% compounded yearly.
→ Time = 1 year.
→ Amount = Principal * [1 + (Rate/100)]^(Time)
Putting all values now, we get,
→ A = 20000[ 1 + (10/100)]¹
→ A = 20000[ 1 + (1/10)]
→ A = 20000[11/10]
→ A = Rs.22,000 .
So,
→ CI = Amount - Principal
→ CI = 22000 - 20000
→ CI = Rs.2000.
_________
since,
→ 2050 > 2000.
Hence, we can conclude that, interest when the rate was compounded half yearly is more than the interest he would get if it was compounded annually .
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Answer:
Case 1) :-
→ Principal = Rs.20000
→ Rate = 10% compounded half yearly. So, R = (10/2) = 5% per yearly .
→ Time = 1 year. ( since rate is half yearly.) Time will be = 1 * 2 = 2 years.
→ Amount = Principal * [1 + (Rate/100)]^(Time)
Putting all values now, we get,
→ A = 20000[ 1 + (5/100)]²
→ A = 20000[ 1 + (1/20)]²
→ A = 20000[21/20]²
→ A = 20000 * (441/400)
→ A = Rs.22050.
Therefore,
→ CI = Amount - Principal
→ CI = 22050 - 20000
→ CI = Rs.2050.
___________
Case 2 :-
→ Principal = Rs.20000
→ Rate = 10% compounded yearly.
→ Time = 1 year.
→ Amount = Principal * [1 + (Rate/100)]^(Time)
Putting all values now, we get,
→ A = 20000[ 1 + (10/100)]¹
→ A = 20000[ 1 + (1/10)]
→ A = 20000[11/10]
→ A = Rs.22,000 .
So,
→ CI = Amount - Principal
→ CI = 22000 - 20000
→ CI = Rs.2000.
_________
since,
→ 2050 > 2000.
Hence, we can conclude that, interest when the rate was compounded half yearly is more than the interest he would get if it was compounded annually .
Step-by-step explanation: