Question

What will Rs. 10000 amount to in 4 years to in 4 years after its deposit in a bank which pays annual interest at the rate of 10% per annum compounded annually ?

Answer 1

Original sum = Rs. 10000.
Amount after 1 year = Rs. `10000+Rs. (10000xx10/100xx1)= Rs. 11000`,
amount after 2 years `=Rs. 11000 + Rs. 11000+Rs. (11000xx10/100xx1)= Rs. 12100`,
amount after 3 years `= Rs. 12100+ Rs. (12100xx10/100xx1)= Rs. 13310`,
and so on.
Thus, these amounts from a GP
`10000, 11000, 12100, 13310, ...`
such that `11000/10000=12100/11000=13310/12100=11/10`.
In this GP, we have `a=10000, r=11/10`.
Amount after 4 years `=T_(5)=ar^((5-1))=ar^(4)`
`=Rs. [10000xx(11/10)^(4)]= Rs. 14641`.
Hence, the amount after 4 years is Rs. 14641.
Alternative method
Here, `P=Rs. 10000, R=10% p.a. and T=4` years.
`:.` amount after 4 years `=Rs. {Pxx(1+R/100)^(T)}`
`= Rs. {10000xx(1+10/100)^(4)}`
`=Rs. {10000xx(11/10)^(4)}= Rs. 14641`.
Hence, the amount after 4 years is Rs. 14641.