Question

In how many years will Rs 4000 amount to Rs 4630.50 at 5% per annum compounded annually ?
Ans - 3 Years but how ???

Answer 1

given..

R = principal amount =4000

c = compounded amount = 4630.5

n= no.of years = ?

i = rate of interest per annum = 5%

we know that c = p((1+i)^n

4530.5 = 4000((1+5%)^n

4530.5=  4000((1+0.05)^n

4530.5 =  4000((1.05)^n

4530.5/4000 =  (1.05)^n

1.132625 =   (1.05)^n

(1.05)^3 = (1.05)^n

powers are equal ..equate the powers....

n = 3.. so no.of uyears are 3

Answer 2

as it is compounded annually the formula for compound interest is

a=p[ 1+r/100]to the power of  n

given

principal = 4000

amount= 4630.50

rate = 5%

time [n] = n

applying the formula we get

                                             

4630.50 = 4000 [1+5/100] to the power of n

4630.50 = 4000[1+1/20] to the power of n

4630.50 = 4000 [21/20] to the power of n

4630.50/4000 = 21/20 to the power of n