Question

Under the rule of seventy, for how many years do you have to deposit € 50000 to get € 100,000 if the deposit rate is 2%?

Answer 1

The Rule of 72 is a simple way to determine how long an investment will take to double given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors obtain a rough estimate of how many years it will take for the initial investment to duplicate itself.

Y = 72 / R and R = 72 / Y

where Y and R are the years and interest rate, respectively.

therefore in the above question to double the initial investment of Euro 50,000 to euro 100,000 at the deposit rate of 2% , it will take 72/2 = 36 Years

and to be precise the exact answer would be 35 years calculated as below:-

Future Value=PV×(1+r)

Where: PV=Present Value

r=Interest Rate

n=Number of Time Periods​

2=1×(1+r)n

2=(1+r)n

Taking Logarithm on both sides ;

ln(2)= n × ln(1+r)

ln(2) = r × n

0.693/r = n

69.3/r%=n

69.3/2 = 34.65 i.e. 35 years