A) time for a lump sum to double, b) time to reach financial goal?

a) If you deposit money today in an account that pays 6.5% annual interest,how long it will yake to double your money?





b) You have $42,180.53 in a broke age account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. you expect to earn 12% annually on account. How many years wiil it take to reach your goal?





Please help me to solve this problem with formula approach, not calculator.|||First you have to kick Obama in the nuts, then you have to figure this problem:





a.) 11.01yrs =(LOG(200/100))/(LOG(1+.065/1))/1





b.) 11 years:





$146,727.08 =42180.53*(1+.12/1)^(1*11)


+


$103,272.92 =5,000.00*(((1+.12/1)^(11*1)-1)/(.12/1))


=


$250,000.00|||A simpler rough approximation of time to double your money is:





72 / %interest = years


For example 72 / 6.5 = a little over 11 years (close enough guesstimate)





Of course taxes lower the effective rate and lengthen the time, unless completely non-taxable.