Puneet took₹2,20,000 from his friend Ramneet at the rate of 12% pa.compound annually for 5/2
years and gave this money to this friend Rajesh at same rate for same time but compound half yearly
Find the earning of Puneet in this transaction.
Answers
Solution :-
→ Principal = Rs.2,20,000
→ Rate = 12% PA compounded annually .
→ Time = (5/2) years. = 2(1/2) years.
→ Amount :- (when time is in Fraction )
- Assume Time whole As = W .
- And, Fraction Time as = F .
- Amount = P [ 1 + (R/100) ]^W * [ 1 + {(F*R)/100} ]
from question we have w = 2 , F = (1/2) .
Putting all values now, we get,
→ Amount = 220000[ 1 + (12/100)]² * [ 1 + (0.5*12)/100 ]
→ Amount = 220000[ 1 + (3/25)]² * [ 1 + (3/50)]
→ Amount = 220000(28/25)² * (53/50)
→ Amount = (220000 * 784 * 53) / (625 * 50)
→ Amount = Rs.292,526.08
So, Puneet has to pay Rs.292,526.08 back to his friend Ramneet.
____________
Case 2)
→ Principal = Rs.2,20,000
→ Rate = 12% PA compounded half yearly = (12/2) = 6% PA.
→ Time = (5/2) years. = (5/2) * 2 = 5 years.
→ Amount = P[ 1 + (R/100)]^Time
Putting all values,
→ Amount = 220000[1 + (6/100)]⁵
→ Amount = 220000[ 1 + (3/50)]⁵
→ Amount = 220000(53/50)⁵
→ Amount = Rs.294,409.62
So, Rajesh has to pay Rs.292,526.08 back to his friend Puneet.
___________
Therefore,
→ Earning of Puneet in this transaction = 294,409.62 - 292,526.08 = Rs.1883.54 (Ans.)
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