how long will it take Rupees 12000 to amount to rupees 20000 at 5% converted quarterly?
Answers
Solution :-
- Principal = Rs.12000
- Amount = Rs.20000
- Rate = 5% Quarterly .
- Time = Let T years.
As we know that, when rate is quarterly, time is Multiply by 4, and rate is divided by 4 .
So,
→ Time = 4 * T = 4T years.
→ Rate = (5/4) % per annum.
→ Interest to be Earned = Amount - Principal = 20000 - 12000 = Rs.8000 .
Now, we know that, Simple interest(SI) is :-
→ SI = (Principal * Rate * Time) / 100
Putting all values now, we get :-
→ 8000 = (12000 * 5 * 4T) / (100 * 4)
→ 8000 = 120 * 5 * T
→ 8000 = 600T
→ 6T = 80
→ 3T = 40
→ T = (40/3) years. = 13(1/3) years = 13 + (1/3 * 12) = 13 years , 4 months . (Ans.)
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If we Assume rate is 5% Compounded Quarterly Than :-
→ Principal = Rs.12000
→Amount = Rs.20000
→ Rate = 5% Quarterly = (5/4) % annually.
→ Time = Let T years. = 4T years.
Than,
→ Amount = Principal * [ 1 + (R/100) ]^(Time)
Putting all values we get ,
→ 20000 = 12000[ 1 + (5/400)]^(4T)
→ (20/12) = [ 1 + (1/80) ]^4T
→ (5/3) = (81/80)^4T
Multiply by log both sides ,
→ log{(5/3)} = 4T * log(81/80)
→ 0.221 = 4T * 0.005
→ 0.02T = 0.221
→ T = (0.221/0.02)
→ T ≈ 11.05 years. (Ans.)