Question 460085
A certain sum is doubled in 50 years by simple interest. At the same rate in which time the sum is doubled by compound interest?  

Let i = the interest rate in %

To double certain sum, total interst should be 100

50*i = 100
   i = 2

If 2% interest is compounded annually, the equation becomes
 (1.02)^x = 2

Log both sides to get

Log (1.02)^x = log 2
x Log 1.02 = Log 2
x = Log 2 / Log 1.02
x = 35


At the same rate, the sum is doubled by compound interest in 35 years.