Question

A sum of money becomes 16 times of itself in 2 years if compounded half yearly. How much time it will take to become 27 times if compounded yearly.

Answer 1

Answer:

Explanation:

Let the Initial principal be P = 100

According To the Question,

P ,R=Compounded half yearly, T=2 yrs= 16P

When Compounded Half Yearly,

R becomes--> R/2 , T  becomes =  2 T.

So, T=2 x 2 = 4.

Amount = P ( 1 + R/100)^n

1600 = 100( 1 + R/200 ) ^ 4

16 = ( 1 + R/200)^4

2 = 1+ R/200

R = 200%

Now, the sum is getting 27 times, R=200%(p.a), T =?

Amount = P ( 1 + R/100)^n

2700 = 100( 1 + 200/100 ) ^ n

27 = (1+2) ^n

3^3 =3^n

Means n = 3 years, it will take 3 years to become 27 times if compounded yearly.