You have just won 170000 from a lottery If you invest all th

You have just won $170,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 6% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)
yr

Solution

We can calculate the time in weeks or in year.

Let’s calculate in weeks.

Weekly interest year = 6/52 = 0.1153846% per week

Initial amount = 170000

Maturity amount = 1,000,000

FV = PV (1 + r)^n

Where,

Future value (FV) = $1000000

Present value (PV) = $170000

Rate of interest (i) = 0.001153846

We need to find the value of (n)

Let\'s put all the values in the formula,

1000000 = 170000 (1 + 0.001153846) ^n

1000000/ 170000 = (1.001153846) ^n

5.88235 = (1.001153846) ^n

To solve this equation we need to apply log on both sides, so the equation will be

log (5.88235) = log (1.001153846) ^n

We know that log (m)^n = n* log (m)

log (5.88235) = n log (1.001153846)

Values of log can be found in the log table, or we can use calculator, so let\'s put the values of logs

0.769550861474431 = n * 0.000500820071680241

n = 0.769550861474431/ 0.000500820071680241

n = 1536.58151

So the value of n is 1536.58

So it will take 1537 weeks.

Or

1537/52 = 29.5 years