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

1234.08 weeks.

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 =
`(0.08)/(52)` ( 1 year = 52 weeks )

A = 1,000,000

By substituting the values,

`1000000=150000(1+(0.08)/(52))^t`

`(1000000)/(150000)=((52+0.08)/(52))^t`

`(20)/(3)=((52.08)/(52))^t`

Taking log both sides,

`log((20)/(3))=t log((52.08)/(52))`

`\implies t = (log((20)/(3)))/( log((52.08)/(52)))=1234.07630713\approx 1234.08`

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