Question

You have just won $150,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 8% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)

Answer 1

Answer:

1234.08 weeks.

Step-by-step explanation:

Since, the amount formula in compound interest is,

$A=P(1+r)^t$

Where, P is the principal amount,

r is the rate per period,

t is the number of periods,

Given,

P = $ 150,000,

Annual rate = 8 % = 0.08,

So, the weekly rate, r = $\frac{0.08}{52}$  ( 1 year = 52 weeks )

A = 1,000,000

By substituting the values,

$1000000=150000(1+\frac{0.08}{52})^t$

$\frac{1000000}{150000}=(\frac{52+0.08}{52})^t$

$\frac{20}{3}=(\frac{52.08}{52})^t$

Taking log both sides,

$log(\frac{20}{3})=t log(\frac{52.08}{52})$

$\implies t = \frac{log(\frac{20}{3})}{ log(\frac{52.08}{52})}=1234.07630713\approx 1234.08$

Hence, for become a millionaire we should wait 1234.08 weeks.