Question

how much time will a sum of money triple itselt at 20% p.a ​

Answer 1

Answer:

10 years . A sum becomes 3 times. Rate = 20%

Answer 2

Let me explain how to work it out for yourself.

As a decimal value, 20% is 0.20. Your gross growth rate is 1+0.20 = 1.20. After n periods, your starting value will be multiplied by 1.20n , and we want to find when this triples our money, so we set it equal to 3.

1.20n=3.00

Now, to isolate an exponent (the n here), a useful function is the logarithm because it has the property that log(ab)=b.log(a) . So, taking the logs of both sides of our equation gives,

log(1.20n)=n.log(1.20)=log(3.00)

∴n=log(3.00)log(1.20)≈6.026

In general to multiply your money X times at growth rate g will take,

n=log(X)log(1+g) periods.

Hope it's helpful to you