Monaj deposited a sum of ₹64000 in the post office for 3 years , compounded annually at 7.5 % per annum . what will he get on maturity?
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Answer:
Manoj deposited a sum of ₹ 64000 in a post office for 3 years, compounded annually at 7½℅ per annum. What amount will he get upon maturity?
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This is a standard question in text books and the answer can be sought by quick google search but still i will try to explain
In questions like these first lets assume the Amount is expressed as Pi where i denotes the amount after ith year. So after the first year it’ll be P1 and the second year it’ll be P2 etc. Lets say the Initial amount is P0 and the annual interest rate is r .
Hence after the first year the amount P1 is
P1=P0(1+r)
after the second year it’ll be
P2=P1(1+r)
third year
P3=P2(1+r)
or P3 in terms of P0 is
P3=P2(1+r)=P1(1+r)(1+r)=P0(1+r)(1+r)(1+r)
or
P3=P03(1+r)3
and Voila! put values for P0=64000,r=0.075 and there you go. Simple isn’t it?
P.S. The above can be generalized to n number of years as
Pn=P0(1+r)n
and carrying this forward will eventually introduce exponential function, the great e .