Question

a sum of money becomes 16 times of itself in 2 years if compounded half yearly how much time take to become 27 time

Answer 1

Answer:

a sum of money becomes 16 times of itself in 2 years if compounded half yearly then it will  take 2.378  Years to become 27 time

Step-by-step explanation:

16P = P( 1 + r/100n)^(nt)

r = rate of interest per annum

n =2 (Compounded half yearly so two times in a year)

t = 2 years

16P = P( 1 + r/200)^(2*2)

=> 16 = ( 1 + r/200)⁴

=> 2⁴ =  ( 1 + r/200)⁴

=> 2 = 1 + r/200

=> 1 = r/200

=> r = 200

rate of interest = 200% per annum

let say in t years amount become 27 times

27P = P(1 + 200/200)^2t

=> 27 = 2^2t

=> log 27 = 2t log 2

=> 2t = log 27 / log 2

=> 2t = 1.431 / 0.301

=> 2t = 4.755

=> t = 2.378  Years

Answer 2

Let money be x

Rate=R % when compounded yearly

But when compounded half yearly

Rate =R/2 & t=2×2=4half year

Now,

16x=x(1+R/200)^4

16×(200)^4=(200+R)^4

(400)^4=(200+R)^4

R=200%

Now ,Amount=27x

27x=x(1+200/2)^n

3^3=3^n

n=3 years Answer

Step-by-step explanation: