You have just received 165000 from the estate of a longlost

You have just received $165,000 from the estate of a long-lost rich uncle. If you invest all your inheritance in a tax-free bond fund earning 6.5% compounded quarterly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)

Solution

FV=PV(1+r)ⁿ Where FV=Future Value, PV=Present Value, r=Rate, n=Number of periods for which you made the payment
Thus n= ln(FV/PV) / ln(1+r)

Given Data:
FV=$1,000,000
PV=$165,000
r=0.065/4 = 0.01625 (As it is compounded quarterly or 4 times a year)
FV/PV=6.0606
n= ln(6.0606)/ln(1.01625) = 111.78 periods (quarters in this case as you are paying quarterly)
Thus 112 quarters corresponds to 111.78/4=27.945 years = 27 years 11 months 11 days (28 years approximately)